The Stigler Diet Problem

In this section, we show how to solve a classic problem called the Stigler diet, named for economics Nobel laureate George Stigler, who computed an inexpensive way to fulfill basic nutritional needs given a set of foods. He posed this as a mathematical exercise, not as eating recommendations, although the notion of computing optimal nutrition has of come into vogue recently.

The Stigler diet mandated that these minimums be met:

Nutrients list

Nutrient Daily Recommended Intake
Calories 3,000 Calories
Protein 70 grams
Calcium .8 grams
Iron 12 milligrams
Vitamin A 5,000 IU
Thiamine (Vitamin B1) 1.8 milligrams
Riboflavin (Vitamin B2) 2.7 milligrams
Niacin 18 milligrams
Ascorbic Acid (Vitamin C) 75 milligrams

The set of foods Stigler evaluated was a reflection of the time (1944). The nutritional data below is per dollar, not per unit, so the objective is to determine how many dollars to spend on each foodstuff.

Commodities list

Commodity Unit 1939 price (cents) Calories (kcal) Protein (g) Calcium (g) Iron (mg) Vitamin A (KIU) Thiamine (mg) Riboflavin (mg) Niacin (mg) Ascorbic Acid (mg)
Wheat Flour (Enriched) 10 lb. 36 44.7 1411 2 365 0 55.4 33.3 441 0
Macaroni 1 lb. 14.1 11.6 418 0.7 54 0 3.2 1.9 68 0
Wheat Cereal (Enriched) 28 oz. 24.2 11.8 377 14.4 175 0 14.4 8.8 114 0
Corn Flakes 8 oz. 7.1 11.4 252 0.1 56 0 13.5 2.3 68 0
Corn Meal 1 lb. 4.6 36.0 897 1.7 99 30.9 17.4 7.9 106 0
Hominy Grits 24 oz. 8.5 28.6 680 0.8 80 0 10.6 1.6 110 0
Rice 1 lb. 7.5 21.2 460 0.6 41 0 2 4.8 60 0
Rolled Oats 1 lb. 7.1 25.3 907 5.1 341 0 37.1 8.9 64 0
White Bread (Enriched) 1 lb. 7.9 15.0 488 2.5 115 0 13.8 8.5 126 0
Whole Wheat Bread 1 lb. 9.1 12.2 484 2.7 125 0 13.9 6.4 160 0
Rye Bread 1 lb. 9.1 12.4 439 1.1 82 0 9.9 3 66 0
Pound Cake 1 lb. 24.8 8.0 130 0.4 31 18.9 2.8 3 17 0
Soda Crackers 1 lb. 15.1 12.5 288 0.5 50 0 0 0 0 0
Milk 1 qt. 11 6.1 310 10.5 18 16.8 4 16 7 177
Evaporated Milk (can) 14.5 oz. 6.7 8.4 422 15.1 9 26 3 23.5 11 60
Butter 1 lb. 30.8 10.8 9 0.2 3 44.2 0 0.2 2 0
Oleomargarine 1 lb. 16.1 20.6 17 0.6 6 55.8 0.2 0 0 0
Eggs 1 doz. 32.6 2.9 238 1.0 52 18.6 2.8 6.5 1 0
Cheese (Cheddar) 1 lb. 24.2 7.4 448 16.4 19 28.1 0.8 10.3 4 0
Cream 1/2 pt. 14.1 3.5 49 1.7 3 16.9 0.6 2.5 0 17
Peanut Butter 1 lb. 17.9 15.7 661 1.0 48 0 9.6 8.1 471 0
Mayonnaise 1/2 pt. 16.7 8.6 18 0.2 8 2.7 0.4 0.5 0 0
Crisco 1 lb. 20.3 20.1 0 0 0 0 0 0 0 0
Lard 1 lb. 9.8 41.7 0 0 0 0.2 0 0.5 5 0
Sirloin Steak 1 lb. 39.6 2.9 166 0.1 34 0.2 2.1 2.9 69 0
Round Steak 1 lb. 36.4 2.2 214 0.1 32 0.4 2.5 2.4 87 0
Rib Roast 1 lb. 29.2 3.4 213 0.1 33 0 0 2 0 0
Chuck Roast 1 lb. 22.6 3.6 309 0.2 46 0.4 1 4 120 0
Plate 1 lb. 14.6 8.5 404 0.2 62 0 0.9 0 0 0
Liver (Beef) 1 lb. 26.8 2.2 333 0.2 139 169.2 6.4 50.8 316 525
Leg of Lamb 1 lb. 27.6 3.1 245 0.1 20 0 2.8 3.9 86 0
Lamb Chops (Rib) 1 lb. 36.6 3.3 140 0.1 15 0 1.7 2.7 54 0
Pork Chops 1 lb. 30.7 3.5 196 0.2 30 0 17.4 2.7 60 0
Pork Loin Roast 1 lb. 24.2 4.4 249 0.3 37 0 18.2 3.6 79 0
Bacon 1 lb. 25.6 10.4 152 0.2 23 0 1.8 1.8 71 0
Ham, smoked 1 lb. 27.4 6.7 212 0.2 31 0 9.9 3.3 50 0
Salt Pork 1 lb. 16 18.8 164 0.1 26 0 1.4 1.8 0 0
Roasting Chicken 1 lb. 30.3 1.8 184 0.1 30 0.1 0.9 1.8 68 46
Veal Cutlets 1 lb. 42.3 1.7 156 0.1 24 0 1.4 2.4 57 0
Salmon, Pink (can) 16 oz. 13 5.8 705 6.8 45 3.5 1 4.9 209 0
Apples 1 lb. 4.4 5.8 27 0.5 36 7.3 3.6 2.7 5 544
Bananas 1 lb. 6.1 4.9 60 0.4 30 17.4 2.5 3.5 28 498
Lemons 1 doz. 26 1.0 21 0.5 14 0 0.5 0 4 952
Oranges 1 doz. 30.9 2.2 40 1.1 18 11.1 3.6 1.3 10 1998
Green Beans 1 lb. 7.1 2.4 138 3.7 80 69 4.3 5.8 37 862
Cabbage 1 lb. 3.7 2.6 125 4.0 36 7.2 9 4.5 26 5369
Carrots 1 bunch 4.7 2.7 73 2.8 43 188.5 6.1 4.3 89 608
Celery 1 stalk 7.3 0.9 51 3.0 23 0.9 1.4 1.4 9 313
Lettuce 1 head 8.2 0.4 27 1.1 22 112.4 1.8 3.4 11 449
Onions 1 lb. 3.6 5.8 166 3.8 59 16.6 4.7 5.9 21 1184
Potatoes 15 lb. 34 14.3 336 1.8 118 6.7 29.4 7.1 198 2522
Spinach 1 lb. 8.1 1.1 106 0 138 918.4 5.7 13.8 33 2755
Sweet Potatoes 1 lb. 5.1 9.6 138 2.7 54 290.7 8.4 5.4 83 1912
Peaches (can) No. 2 1/2 16.8 3.7 20 0.4 10 21.5 0.5 1 31 196
Pears (can) No. 2 1/2 20.4 3.0 8 0.3 8 0.8 0.8 0.8 5 81
Pineapple (can) No. 2 1/2 21.3 2.4 16 0.4 8 2 2.8 0.8 7 399
Asparagus (can) No. 2 27.7 0.4 33 0.3 12 16.3 1.4 2.1 17 272
Green Beans (can) No. 2 10 1.0 54 2 65 53.9 1.6 4.3 32 431
Pork and Beans (can) 16 oz. 7.1 7.5 364 4 134 3.5 8.3 7.7 56 0
Corn (can) No. 2 10.4 5.2 136 0.2 16 12 1.6 2.7 42 218
Peas (can) No. 2 13.8 2.3 136 0.6 45 34.9 4.9 2.5 37 370
Tomatoes (can) No. 2 8.6 1.3 63 0.7 38 53.2 3.4 2.5 36 1253
Tomato Soup (can) 10 1/2 oz. 7.6 1.6 71 0.6 43 57.9 3.5 2.4 67 862
Peaches, Dried 1 lb. 15.7 8.5 87 1.7 173 86.8 1.2 4.3 55 57
Prunes, Dried 1 lb. 9 12.8 99 2.5 154 85.7 3.9 4.3 65 257
Raisins, Dried 15 oz. 9.4 13.5 104 2.5 136 4.5 6.3 1.4 24 136
Peas, Dried 1 lb. 7.9 20.0 1367 4.2 345 2.9 28.7 18.4 162 0
Lima Beans, Dried 1 lb. 8.9 17.4 1055 3.7 459 5.1 26.9 38.2 93 0
Navy Beans, Dried 1 lb. 5.9 26.9 1691 11.4 792 0 38.4 24.6 217 0
Coffee 1 lb. 22.4 0 0 0 0 0 4 5.1 50 0
Tea 1/4 lb. 17.4 0 0 0 0 0 0 2.3 42 0
Cocoa 8 oz. 8.6 8.7 237 3 72 0 2 11.9 40 0
Chocolate 8 oz. 16.2 8.0 77 1.3 39 0 0.9 3.4 14 0
Sugar 10 lb. 51.7 34.9 0 0 0 0 0 0 0 0
Corn Syrup 24 oz. 13.7 14.7 0 0.5 74 0 0 0 5 0
Molasses 18 oz. 13.6 9.0 0 10.3 244 0 1.9 7.5 146 0
Strawberry Preserves 1 lb. 20.5 6.4 11 0.4 7 0.2 0.2 0.4 3 0

Since the nutrients have all been normalized by price, our objective is simply minimizing the sum of foods.

In 1944, Stigler calculated the best answer he could, noting with sadness:

"...there does not appear to be any direct method of finding the minimum of a linear function subject to linear conditions."

He found a diet that cost $39.93 per year, in 1939 dollars. In 1947, Jack Laderman used the simplex method (then, a recent invention!) to determine the optimal solution. It took 120 man days of nine clerks on desk calculators to arrive at the answer.

Solution using the linear solver

The following sections present a program that solves the Stigler diet problem.

Import the linear solver wrapper

Import the OR-Tools linear solver wrapper, an interface for the Glop linear solver, as shown below.

Python

from ortools.linear_solver import pywraplp

C++

#include <array>
#include <string>
#include <utility>  // std::pair
#include <vector>

#include "absl/flags/flag.h"
#include "absl/flags/parse.h"
#include "absl/flags/usage.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.h"

Java

import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.util.ArrayList;
import java.util.List;

C#

using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;

Data for the problem

The following code creates an array nutrients for the minimum nutrient requirements , and an array data for the nutritional data table in any solution.

Python

# Nutrient minimums.
nutrients = [
    ['Calories (kcal)', 3],
    ['Protein (g)', 70],
    ['Calcium (g)', 0.8],
    ['Iron (mg)', 12],
    ['Vitamin A (KIU)', 5],
    ['Vitamin B1 (mg)', 1.8],
    ['Vitamin B2 (mg)', 2.7],
    ['Niacin (mg)', 18],
    ['Vitamin C (mg)', 75],
]

# Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g),
# Calcium (g), Iron (mg), Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg),
# Niacin (mg), Vitamin C (mg)
data = [
    [
        'Wheat Flour (Enriched)', '10 lb.', 36, 44.7, 1411, 2, 365, 0, 55.4,
        33.3, 441, 0
    ],
    ['Macaroni', '1 lb.', 14.1, 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0],
    [
        'Wheat Cereal (Enriched)', '28 oz.', 24.2, 11.8, 377, 14.4, 175, 0,
        14.4, 8.8, 114, 0
    ],
    ['Corn Flakes', '8 oz.', 7.1, 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0],
    [
        'Corn Meal', '1 lb.', 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106,
        0
    ],
    [
        'Hominy Grits', '24 oz.', 8.5, 28.6, 680, 0.8, 80, 0, 10.6, 1.6,
        110, 0
    ],
    ['Rice', '1 lb.', 7.5, 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0],
    ['Rolled Oats', '1 lb.', 7.1, 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0],
    [
        'White Bread (Enriched)', '1 lb.', 7.9, 15.0, 488, 2.5, 115, 0,
        13.8, 8.5, 126, 0
    ],
    [
        'Whole Wheat Bread', '1 lb.', 9.1, 12.2, 484, 2.7, 125, 0, 13.9,
        6.4, 160, 0
    ],
    ['Rye Bread', '1 lb.', 9.1, 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0],
    ['Pound Cake', '1 lb.', 24.8, 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0],
    ['Soda Crackers', '1 lb.', 15.1, 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0],
    ['Milk', '1 qt.', 11, 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177],
    [
        'Evaporated Milk (can)', '14.5 oz.', 6.7, 8.4, 422, 15.1, 9, 26, 3,
        23.5, 11, 60
    ],
    ['Butter', '1 lb.', 30.8, 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0],
    ['Oleomargarine', '1 lb.', 16.1, 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0],
    ['Eggs', '1 doz.', 32.6, 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0],
    [
        'Cheese (Cheddar)', '1 lb.', 24.2, 7.4, 448, 16.4, 19, 28.1, 0.8,
        10.3, 4, 0
    ],
    ['Cream', '1/2 pt.', 14.1, 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17],
    [
        'Peanut Butter', '1 lb.', 17.9, 15.7, 661, 1.0, 48, 0, 9.6, 8.1,
        471, 0
    ],
    ['Mayonnaise', '1/2 pt.', 16.7, 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0],
    ['Crisco', '1 lb.', 20.3, 20.1, 0, 0, 0, 0, 0, 0, 0, 0],
    ['Lard', '1 lb.', 9.8, 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0],
    [
        'Sirloin Steak', '1 lb.', 39.6, 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9,
        69, 0
    ],
    ['Round Steak', '1 lb.', 36.4, 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0],
    ['Rib Roast', '1 lb.', 29.2, 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0],
    ['Chuck Roast', '1 lb.', 22.6, 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0],
    ['Plate', '1 lb.', 14.6, 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0],
    [
        'Liver (Beef)', '1 lb.', 26.8, 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8,
        316, 525
    ],
    ['Leg of Lamb', '1 lb.', 27.6, 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0],
    [
        'Lamb Chops (Rib)', '1 lb.', 36.6, 3.3, 140, 0.1, 15, 0, 1.7, 2.7,
        54, 0
    ],
    ['Pork Chops', '1 lb.', 30.7, 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0],
    [
        'Pork Loin Roast', '1 lb.', 24.2, 4.4, 249, 0.3, 37, 0, 18.2, 3.6,
        79, 0
    ],
    ['Bacon', '1 lb.', 25.6, 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0],
    ['Ham, smoked', '1 lb.', 27.4, 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0],
    ['Salt Pork', '1 lb.', 16, 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0],
    [
        'Roasting Chicken', '1 lb.', 30.3, 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8,
        68, 46
    ],
    ['Veal Cutlets', '1 lb.', 42.3, 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0],
    [
        'Salmon, Pink (can)', '16 oz.', 13, 5.8, 705, 6.8, 45, 3.5, 1, 4.9,
        209, 0
    ],
    ['Apples', '1 lb.', 4.4, 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544],
    ['Bananas', '1 lb.', 6.1, 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498],
    ['Lemons', '1 doz.', 26, 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952],
    ['Oranges', '1 doz.', 30.9, 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998],
    ['Green Beans', '1 lb.', 7.1, 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862],
    ['Cabbage', '1 lb.', 3.7, 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369],
    ['Carrots', '1 bunch', 4.7, 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608],
    ['Celery', '1 stalk', 7.3, 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313],
    ['Lettuce', '1 head', 8.2, 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449],
    ['Onions', '1 lb.', 3.6, 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184],
    [
        'Potatoes', '15 lb.', 34, 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198,
        2522
    ],
    ['Spinach', '1 lb.', 8.1, 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755],
    [
        'Sweet Potatoes', '1 lb.', 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4,
        83, 1912
    ],
    [
        'Peaches (can)', 'No. 2 1/2', 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5, 1,
        31, 196
    ],
    [
        'Pears (can)', 'No. 2 1/2', 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5,
        81
    ],
    [
        'Pineapple (can)', 'No. 2 1/2', 21.3, 2.4, 16, 0.4, 8, 2, 2.8, 0.8,
        7, 399
    ],
    [
        'Asparagus (can)', 'No. 2', 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1,
        17, 272
    ],
    [
        'Green Beans (can)', 'No. 2', 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3,
        32, 431
    ],
    [
        'Pork and Beans (can)', '16 oz.', 7.1, 7.5, 364, 4, 134, 3.5, 8.3,
        7.7, 56, 0
    ],
    ['Corn (can)', 'No. 2', 10.4, 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218],
    [
        'Peas (can)', 'No. 2', 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37,
        370
    ],
    [
        'Tomatoes (can)', 'No. 2', 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5,
        36, 1253
    ],
    [
        'Tomato Soup (can)', '10 1/2 oz.', 7.6, 1.6, 71, 0.6, 43, 57.9, 3.5,
        2.4, 67, 862
    ],
    [
        'Peaches, Dried', '1 lb.', 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3,
        55, 57
    ],
    [
        'Prunes, Dried', '1 lb.', 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65,
        257
    ],
    [
        'Raisins, Dried', '15 oz.', 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4,
        24, 136
    ],
    [
        'Peas, Dried', '1 lb.', 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4,
        162, 0
    ],
    [
        'Lima Beans, Dried', '1 lb.', 8.9, 17.4, 1055, 3.7, 459, 5.1, 26.9,
        38.2, 93, 0
    ],
    [
        'Navy Beans, Dried', '1 lb.', 5.9, 26.9, 1691, 11.4, 792, 0, 38.4,
        24.6, 217, 0
    ],
    ['Coffee', '1 lb.', 22.4, 0, 0, 0, 0, 0, 4, 5.1, 50, 0],
    ['Tea', '1/4 lb.', 17.4, 0, 0, 0, 0, 0, 0, 2.3, 42, 0],
    ['Cocoa', '8 oz.', 8.6, 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0],
    ['Chocolate', '8 oz.', 16.2, 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0],
    ['Sugar', '10 lb.', 51.7, 34.9, 0, 0, 0, 0, 0, 0, 0, 0],
    ['Corn Syrup', '24 oz.', 13.7, 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0],
    ['Molasses', '18 oz.', 13.6, 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0],
    [
        'Strawberry Preserves', '1 lb.', 20.5, 6.4, 11, 0.4, 7, 0.2, 0.2,
        0.4, 3, 0
    ],
]

C++

// Nutrient minimums.
const std::vector<std::pair<std::string, double>> nutrients = {
    {"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
    {"Calcium (g)", 0.8},     {"Iron (mg)", 12.0},
    {"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
    {"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
    {"Vitamin C (mg)", 75.0}};

struct Commodity {
  std::string name;  //!< Commodity name
  std::string unit;  //!< Unit
  double price;      //!< 1939 price per unit (cents)
  //! Calories (kcal),
  //! Protein (g),
  //! Calcium (g),
  //! Iron (mg),
  //! Vitamin A (kIU),
  //! Vitamin B1 (mg),
  //! Vitamin B2 (mg),
  //! Niacin (mg),
  //! Vitamin C (mg)
  std::array<double, 9> nutrients;
};

std::vector<Commodity> data = {
    {"Wheat Flour (Enriched)",
     "10 lb.",
     36,
     {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}},
    {"Macaroni", "1 lb.", 14.1, {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}},
    {"Wheat Cereal (Enriched)",
     "28 oz.",
     24.2,
     {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}},
    {"Corn Flakes", "8 oz.", 7.1, {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}},
    {"Corn Meal",
     "1 lb.",
     4.6,
     {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}},
    {"Hominy Grits",
     "24 oz.",
     8.5,
     {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}},
    {"Rice", "1 lb.", 7.5, {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}},
    {"Rolled Oats", "1 lb.", 7.1, {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}},
    {"White Bread (Enriched)",
     "1 lb.",
     7.9,
     {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}},
    {"Whole Wheat Bread",
     "1 lb.",
     9.1,
     {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}},
    {"Rye Bread", "1 lb.", 9.1, {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}},
    {"Pound Cake", "1 lb.", 24.8, {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}},
    {"Soda Crackers", "1 lb.", 15.1, {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}},
    {"Milk", "1 qt.", 11, {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}},
    {"Evaporated Milk (can)",
     "14.5 oz.",
     6.7,
     {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}},
    {"Butter", "1 lb.", 30.8, {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}},
    {"Oleomargarine", "1 lb.", 16.1, {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}},
    {"Eggs", "1 doz.", 32.6, {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}},
    {"Cheese (Cheddar)",
     "1 lb.",
     24.2,
     {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}},
    {"Cream", "1/2 pt.", 14.1, {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}},
    {"Peanut Butter",
     "1 lb.",
     17.9,
     {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}},
    {"Mayonnaise", "1/2 pt.", 16.7, {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}},
    {"Crisco", "1 lb.", 20.3, {20.1, 0, 0, 0, 0, 0, 0, 0, 0}},
    {"Lard", "1 lb.", 9.8, {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}},
    {"Sirloin Steak",
     "1 lb.",
     39.6,
     {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}},
    {"Round Steak", "1 lb.", 36.4, {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}},
    {"Rib Roast", "1 lb.", 29.2, {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}},
    {"Chuck Roast", "1 lb.", 22.6, {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}},
    {"Plate", "1 lb.", 14.6, {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}},
    {"Liver (Beef)",
     "1 lb.",
     26.8,
     {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}},
    {"Leg of Lamb", "1 lb.", 27.6, {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}},
    {"Lamb Chops (Rib)",
     "1 lb.",
     36.6,
     {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}},
    {"Pork Chops", "1 lb.", 30.7, {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}},
    {"Pork Loin Roast",
     "1 lb.",
     24.2,
     {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}},
    {"Bacon", "1 lb.", 25.6, {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}},
    {"Ham, smoked", "1 lb.", 27.4, {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}},
    {"Salt Pork", "1 lb.", 16, {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}},
    {"Roasting Chicken",
     "1 lb.",
     30.3,
     {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}},
    {"Veal Cutlets", "1 lb.", 42.3, {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}},
    {"Salmon, Pink (can)",
     "16 oz.",
     13,
     {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}},
    {"Apples", "1 lb.", 4.4, {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}},
    {"Bananas", "1 lb.", 6.1, {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}},
    {"Lemons", "1 doz.", 26, {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}},
    {"Oranges", "1 doz.", 30.9, {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}},
    {"Green Beans", "1 lb.", 7.1, {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}},
    {"Cabbage", "1 lb.", 3.7, {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}},
    {"Carrots", "1 bunch", 4.7, {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}},
    {"Celery", "1 stalk", 7.3, {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}},
    {"Lettuce", "1 head", 8.2, {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}},
    {"Onions", "1 lb.", 3.6, {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}},
    {"Potatoes",
     "15 lb.",
     34,
     {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}},
    {"Spinach", "1 lb.", 8.1, {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}},
    {"Sweet Potatoes",
     "1 lb.",
     5.1,
     {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}},
    {"Peaches (can)",
     "No. 2 1/2",
     16.8,
     {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}},
    {"Pears (can)",
     "No. 2 1/2",
     20.4,
     {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}},
    {"Pineapple (can)",
     "No. 2 1/2",
     21.3,
     {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}},
    {"Asparagus (can)",
     "No. 2",
     27.7,
     {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}},
    {"Green Beans (can)",
     "No. 2",
     10,
     {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}},
    {"Pork and Beans (can)",
     "16 oz.",
     7.1,
     {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}},
    {"Corn (can)", "No. 2", 10.4, {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}},
    {"Peas (can)",
     "No. 2",
     13.8,
     {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}},
    {"Tomatoes (can)",
     "No. 2",
     8.6,
     {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}},
    {"Tomato Soup (can)",
     "10 1/2 oz.",
     7.6,
     {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}},
    {"Peaches, Dried",
     "1 lb.",
     15.7,
     {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}},
    {"Prunes, Dried",
     "1 lb.",
     9,
     {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}},
    {"Raisins, Dried",
     "15 oz.",
     9.4,
     {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}},
    {"Peas, Dried",
     "1 lb.",
     7.9,
     {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}},
    {"Lima Beans, Dried",
     "1 lb.",
     8.9,
     {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}},
    {"Navy Beans, Dried",
     "1 lb.",
     5.9,
     {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}},
    {"Coffee", "1 lb.", 22.4, {0, 0, 0, 0, 0, 4, 5.1, 50, 0}},
    {"Tea", "1/4 lb.", 17.4, {0, 0, 0, 0, 0, 0, 2.3, 42, 0}},
    {"Cocoa", "8 oz.", 8.6, {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}},
    {"Chocolate", "8 oz.", 16.2, {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}},
    {"Sugar", "10 lb.", 51.7, {34.9, 0, 0, 0, 0, 0, 0, 0, 0}},
    {"Corn Syrup", "24 oz.", 13.7, {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}},
    {"Molasses", "18 oz.", 13.6, {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}},
    {"Strawberry Preserves",
     "1 lb.",
     20.5,
     {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}}};

Java

// Nutrient minimums.
List<Object[]> nutrients = new ArrayList<>();
nutrients.add(new Object[] {"Calories (kcal)", 3.0});
nutrients.add(new Object[] {"Protein (g)", 70.0});
nutrients.add(new Object[] {"Calcium (g)", 0.8});
nutrients.add(new Object[] {"Iron (mg)", 12.0});
nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
nutrients.add(new Object[] {"Niacin (mg)", 18.0});
nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});

List<Object[]> data = new ArrayList<>();
data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
    new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
data.add(new Object[] {
    "Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
    new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
data.add(new Object[] {
    "Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
data.add(new Object[] {
    "Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
data.add(new Object[] {
    "Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
data.add(
    new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
data.add(new Object[] {
    "Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
    new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
    new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
data.add(new Object[] {
    "Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
data.add(new Object[] {
    "Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
data.add(new Object[] {
    "Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
data.add(
    new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
    new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
data.add(
    new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
data.add(new Object[] {
    "Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
data.add(new Object[] {
    "Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
    new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
data.add(new Object[] {
    "Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
data.add(new Object[] {
    "Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
data.add(new Object[] {
    "Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
data.add(new Object[] {
    "Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
data.add(new Object[] {
    "Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
data.add(
    new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
data.add(new Object[] {
    "Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
data.add(
    new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
    new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
data.add(new Object[] {
    "Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
data.add(new Object[] {
    "Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
data.add(new Object[] {
    "Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
data.add(new Object[] {
    "Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
data.add(new Object[] {
    "Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
data.add(new Object[] {
    "Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
data.add(new Object[] {
    "Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
    new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
data.add(new Object[] {
    "Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
data.add(new Object[] {
    "Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
data.add(new Object[] {
    "Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
data.add(new Object[] {
    "Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
data.add(
    new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
data.add(new Object[] {
    "Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
data.add(new Object[] {
    "Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
data.add(new Object[] {
    "Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
data.add(new Object[] {
    "Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
data.add(new Object[] {
    "Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
data.add(new Object[] {
    "Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
data.add(new Object[] {
    "Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
data.add(new Object[] {
    "Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
data.add(new Object[] {
    "Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
    new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
    new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
data.add(new Object[] {
    "Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
data.add(new Object[] {
    "Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
    new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
data.add(new Object[] {
    "Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
    new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
data.add(new Object[] {
    "Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
data.add(new Object[] {
    "Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
data.add(new Object[] {
    "Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
    new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
data.add(new Object[] {
    "Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
data.add(new Object[] {
    "Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
    new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
data.add(new Object[] {
    "Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
    new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
    new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
data.add(
    new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
data.add(new Object[] {
    "Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {
    "Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
data.add(new Object[] {
    "Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
    new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});

C#

// Nutrient minimums.
(String Name, double Value)[] nutrients =
    new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0),    ("Calcium (g)", 0.8),
            ("Iron (mg)", 12.0),      ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
            ("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0),    ("Vitamin C (mg)", 75.0) };

(String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
    ("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
    ("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
    ("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
    ("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
    ("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
    ("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
    ("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
    ("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
    ("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
    ("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
    ("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
    ("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
    ("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
    ("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
    ("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
    ("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
    ("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
    ("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
    ("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
    ("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
    ("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
    ("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
    ("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
    ("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
    ("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
    ("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
    ("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
    ("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
    ("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
    ("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
    ("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
    ("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
    ("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
    ("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
    ("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
    ("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
    ("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
    ("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
    ("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
    ("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
    ("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
    ("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
    ("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
    ("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
    ("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
    ("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
    ("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
    ("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
    ("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
    ("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
    ("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
    ("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
    ("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
    ("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
    ("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
    ("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
    ("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
    ("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
    ("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
    ("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
    ("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
    ("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
    ("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
    ("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
    ("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
    ("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
    ("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
    ("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
    ("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
    ("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
    ("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
    ("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
    ("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
    ("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
    ("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
    ("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
    ("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
};

Declare the LP solver

The following code instantiates the MPsolver wrapper.

Python

# Instantiate a Glop solver and naming it.
solver = pywraplp.Solver('StiglerDietExample',
                         pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

C++

// Create the linear solver with the GLOP backend.
std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));

Java

// Create the linear solver with the GLOP backend.
MPSolver solver = MPSolver.createSolver("GLOP");
if (solver == null) {
  System.out.println("Could not create solver GLOP");
  return;
}

C#

// Create the linear solver with the GLOP backend.
Solver solver = Solver.CreateSolver("GLOP");

Note: If you install OR-Tools from source, there are other third-party solvers available. See the "Install from Source" section of the installation guide for your platform.

Create the variables

The following code creates the variables for the problem.

Python

# Declare an array to hold our variables.
foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]

print('Number of variables =', solver.NumVariables())

C++

std::vector<MPVariable*> foods;
const double infinity = solver->infinity();
for (const Commodity& commodity : data) {
  foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
}
LOG(INFO) << "Number of variables = " << solver->NumVariables();

Java

double infinity = java.lang.Double.POSITIVE_INFINITY;
List<MPVariable> foods = new ArrayList<>();
for (int i = 0; i < data.size(); ++i) {
  foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
}
System.out.println("Number of variables = " + solver.numVariables());

C#

List<Variable> foods = new List<Variable>();
for (int i = 0; i < data.Length; ++i)
{
    foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
}
Console.WriteLine($"Number of variables = {solver.NumVariables()}");

The method MakeNumVar creates one variable, food[i], for each row of the table. As mentioned previously, the nutritional data is per dollar, so food[i] is the amount of money to spend on commodity i.

Define the constraints

The constraints for Stigler diet require the total amount of the nutrients provided by all foods to be at least the minimum requirement for each nutrient. Next, we write these constraints as inequalities involving the arrays data and nutrients, and the variables food[i].

First, the amount of nutrient i provided by food j per dollar is data[j][i+3] (we add 3 to the column index because the nutrient data begins in the fourth column of data.) Since the amount of money to be spent on food j is food[j], the amount of nutrient i provided by food j is \( data[j][i+3] \cdot food[j] \). Finally, since the minimum requirement for nutrient i is nutrients[i][1], we can write constraint i as follows: \[ \sum_{j} data[j][i+3] \cdot food[j] \geq nutrients[i][1] \;\;\;\;\; (1) \] The following code defines these constraints.

Python

# Create the constraints, one per nutrient.
constraints = []
for i, nutrient in enumerate(nutrients):
    constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
    for j, item in enumerate(data):
        constraints[i].SetCoefficient(foods[j], item[i + 3])

print('Number of constraints =', solver.NumConstraints())

C++

// Create the constraints, one per nutrient.
std::vector<MPConstraint*> constraints;
for (std::size_t i = 0; i < nutrients.size(); ++i) {
  constraints.push_back(
      solver->MakeRowConstraint(nutrients[i].second, infinity));
  for (std::size_t j = 0; j < data.size(); ++j) {
    constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
  }
}
LOG(INFO) << "Number of constraints = " << solver->NumConstraints();

Java

MPConstraint[] constraints = new MPConstraint[nutrients.size()];
for (int i = 0; i < nutrients.size(); ++i) {
  constraints[i] = solver.makeConstraint(
      (double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
  for (int j = 0; j < data.size(); ++j) {
    constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
  }
  // constraints.add(constraint);
}
System.out.println("Number of constraints = " + solver.numConstraints());

C#

List<Constraint> constraints = new List<Constraint>();
for (int i = 0; i < nutrients.Length; ++i)
{
    Constraint constraint =
        solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
    for (int j = 0; j < data.Length; ++j)
    {
        constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
    }
    constraints.Add(constraint);
}
Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");
The Python method Constraint (corresponding to the C++ method MakeRowConstraint) creates the constraints for the problem. For each i,
constraint(nutrients[i][1], solver.infinity)

This creates a constraint in which a linear combination of the variables food[j] (defined next) is greater than or equal to nutrients[i][1]. The coefficients of the linear expression are defined by the method SetCoefficientas follows:

SetCoefficient(food[j], data[j][i+3]

This sets the coefficient of food[j] to be data[j][i+3].

Putting this all together, the code defines the constraints expressed in (1) above.

Create the objective

The following code defines the objective function for the problem.

Python

# Objective function: Minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for food in foods:
    objective.SetCoefficient(food, 1)
objective.SetMinimization()

C++

MPObjective* const objective = solver->MutableObjective();
for (size_t i = 0; i < data.size(); ++i) {
  objective->SetCoefficient(foods[i], 1);
}
objective->SetMinimization();

Java

MPObjective objective = solver.objective();
for (int i = 0; i < data.size(); ++i) {
  objective.setCoefficient(foods.get(i), 1);
}
objective.setMinimization();

C#

Objective objective = solver.Objective();
for (int i = 0; i < data.Length; ++i)
{
    objective.SetCoefficient(foods[i], 1);
}
objective.SetMinimization();

The objective function is the total cost of the food, which is the sum of the variables food[i].

The method SetCoefficient sets the coefficients of the objective function, which are all 1 in this case. Finally, the SetMinimization declares this to be a minimization problem.

Invoke the solver

The following code invokes the solver.

Python

status = solver.Solve()

C++

const MPSolver::ResultStatus result_status = solver->Solve();

Java

final MPSolver.ResultStatus resultStatus = solver.solve();

C#

Solver.ResultStatus resultStatus = solver.Solve();

Glop solves the problem on a typical computer in less than 300 milliseconds:

Display the solution

The following code displays the solution.

Python

# Check that the problem has an optimal solution.
if status != solver.OPTIMAL:
    print('The problem does not have an optimal solution!')
    if status == solver.FEASIBLE:
        print('A potentially suboptimal solution was found.')
    else:
        print('The solver could not solve the problem.')
        exit(1)

# Display the amounts (in dollars) to purchase of each food.
nutrients_result = [0] * len(nutrients)
print('\nAnnual Foods:')
for i, food in enumerate(foods):
    if food.solution_value() > 0.0:
        print('{}: ${}'.format(data[i][0], 365. * food.solution_value()))
        for j, _ in enumerate(nutrients):
            nutrients_result[j] += data[i][j + 3] * food.solution_value()
print('\nOptimal annual price: ${:.4f}'.format(365. * objective.Value()))

print('\nNutrients per day:')
for i, nutrient in enumerate(nutrients):
    print('{}: {:.2f} (min {})'.format(nutrient[0], nutrients_result[i],
                                       nutrient[1]))

C++

// Check that the problem has an optimal solution.
if (result_status != MPSolver::OPTIMAL) {
  LOG(INFO) << "The problem does not have an optimal solution!";
  if (result_status == MPSolver::FEASIBLE) {
    LOG(INFO) << "A potentially suboptimal solution was found";
  } else {
    LOG(INFO) << "The solver could not solve the problem.";
    return;
  }
}

std::vector<double> nutrients_result(nutrients.size());
LOG(INFO) << "";
LOG(INFO) << "Annual Foods:";
for (std::size_t i = 0; i < data.size(); ++i) {
  if (foods[i]->solution_value() > 0.0) {
    LOG(INFO) << data[i].name << ": $"
              << std::to_string(365. * foods[i]->solution_value());
    for (std::size_t j = 0; j < nutrients.size(); ++j) {
      nutrients_result[j] +=
          data[i].nutrients[j] * foods[i]->solution_value();
    }
  }
}
LOG(INFO) << "";
LOG(INFO) << "Optimal annual price: $"
          << std::to_string(365. * objective->Value());
LOG(INFO) << "";
LOG(INFO) << "Nutrients per day:";
for (std::size_t i = 0; i < nutrients.size(); ++i) {
  LOG(INFO) << nutrients[i].first << ": "
            << std::to_string(nutrients_result[i]) << " (min "
            << std::to_string(nutrients[i].second) << ")";
}

Java

// Check that the problem has an optimal solution.
if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
  System.err.println("The problem does not have an optimal solution!");
  if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
    System.err.println("A potentially suboptimal solution was found.");
  } else {
    System.err.println("The solver could not solve the problem.");
    return;
  }
}

// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.size()];
System.out.println("\nAnnual Foods:");
for (int i = 0; i < foods.size(); ++i) {
  if (foods.get(i).solutionValue() > 0.0) {
    System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
    for (int j = 0; j < nutrients.size(); ++j) {
      nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
    }
  }
}
System.out.println("\nOptimal annual price: $" + 365 * objective.value());

System.out.println("\nNutrients per day:");
for (int i = 0; i < nutrients.size(); ++i) {
  System.out.println(
      nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
}

C#

// Check that the problem has an optimal solution.
if (resultStatus != Solver.ResultStatus.OPTIMAL)
{
    Console.WriteLine("The problem does not have an optimal solution!");
    if (resultStatus == Solver.ResultStatus.FEASIBLE)
    {
        Console.WriteLine("A potentially suboptimal solution was found.");
    }
    else
    {
        Console.WriteLine("The solver could not solve the problem.");
        return;
    }
}

// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.Length];
Console.WriteLine("\nAnnual Foods:");
for (int i = 0; i < foods.Count; ++i)
{
    if (foods[i].SolutionValue() > 0.0)
    {
        Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
        for (int j = 0; j < nutrients.Length; ++j)
        {
            nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
        }
    }
}
Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");

Console.WriteLine("\nNutrients per day:");
for (int i = 0; i < nutrients.Length; ++i)
{
    Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
}

Here is the output of the program.

$ make rpy_stigler_diet
"/usr/bin/python3.9" ortools/linear_solver/samples/stigler_diet.py
Number of variables = 77
Number of constraints = 9

Annual Foods:
Wheat Flour (Enriched): $10.774457511918223
Liver (Beef): $0.6907834111074193
Cabbage: $4.093268864842877
Spinach: $1.8277960703546996
Navy Beans, Dried: $22.275425687243036

Optimal annual price: $39.6617

Nutrients per day:
Calories (kcal): 3.00 (min 3)
Protein (g): 147.41 (min 70)
Calcium (g): 0.80 (min 0.8)
Iron (mg): 60.47 (min 12)
Vitamin A (KIU): 5.00 (min 5)
Vitamin B1 (mg): 4.12 (min 1.8)
Vitamin B2 (mg): 2.70 (min 2.7)
Niacin (mg): 27.32 (min 18)
Vitamin C (mg): 75.00 (min 75)

Advanced usage:
Problem solved in  1  milliseconds
Problem solved in  14  iterations

Complete code for the program

The complete code for the Stigler diet program is shown below.

Python

"""The Stigler diet problem.

A description of the problem can be found here:
https://en.wikipedia.org/wiki/Stigler_diet.
"""
from ortools.linear_solver import pywraplp


def main():
    """Entry point of the program."""
    # Instantiate the data problem.
    # Nutrient minimums.
    nutrients = [
        ['Calories (kcal)', 3],
        ['Protein (g)', 70],
        ['Calcium (g)', 0.8],
        ['Iron (mg)', 12],
        ['Vitamin A (KIU)', 5],
        ['Vitamin B1 (mg)', 1.8],
        ['Vitamin B2 (mg)', 2.7],
        ['Niacin (mg)', 18],
        ['Vitamin C (mg)', 75],
    ]

    # Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g),
    # Calcium (g), Iron (mg), Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg),
    # Niacin (mg), Vitamin C (mg)
    data = [
        [
            'Wheat Flour (Enriched)', '10 lb.', 36, 44.7, 1411, 2, 365, 0, 55.4,
            33.3, 441, 0
        ],
        ['Macaroni', '1 lb.', 14.1, 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0],
        [
            'Wheat Cereal (Enriched)', '28 oz.', 24.2, 11.8, 377, 14.4, 175, 0,
            14.4, 8.8, 114, 0
        ],
        ['Corn Flakes', '8 oz.', 7.1, 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0],
        [
            'Corn Meal', '1 lb.', 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106,
            0
        ],
        [
            'Hominy Grits', '24 oz.', 8.5, 28.6, 680, 0.8, 80, 0, 10.6, 1.6,
            110, 0
        ],
        ['Rice', '1 lb.', 7.5, 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0],
        ['Rolled Oats', '1 lb.', 7.1, 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0],
        [
            'White Bread (Enriched)', '1 lb.', 7.9, 15.0, 488, 2.5, 115, 0,
            13.8, 8.5, 126, 0
        ],
        [
            'Whole Wheat Bread', '1 lb.', 9.1, 12.2, 484, 2.7, 125, 0, 13.9,
            6.4, 160, 0
        ],
        ['Rye Bread', '1 lb.', 9.1, 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0],
        ['Pound Cake', '1 lb.', 24.8, 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0],
        ['Soda Crackers', '1 lb.', 15.1, 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0],
        ['Milk', '1 qt.', 11, 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177],
        [
            'Evaporated Milk (can)', '14.5 oz.', 6.7, 8.4, 422, 15.1, 9, 26, 3,
            23.5, 11, 60
        ],
        ['Butter', '1 lb.', 30.8, 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0],
        ['Oleomargarine', '1 lb.', 16.1, 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0],
        ['Eggs', '1 doz.', 32.6, 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0],
        [
            'Cheese (Cheddar)', '1 lb.', 24.2, 7.4, 448, 16.4, 19, 28.1, 0.8,
            10.3, 4, 0
        ],
        ['Cream', '1/2 pt.', 14.1, 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17],
        [
            'Peanut Butter', '1 lb.', 17.9, 15.7, 661, 1.0, 48, 0, 9.6, 8.1,
            471, 0
        ],
        ['Mayonnaise', '1/2 pt.', 16.7, 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0],
        ['Crisco', '1 lb.', 20.3, 20.1, 0, 0, 0, 0, 0, 0, 0, 0],
        ['Lard', '1 lb.', 9.8, 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0],
        [
            'Sirloin Steak', '1 lb.', 39.6, 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9,
            69, 0
        ],
        ['Round Steak', '1 lb.', 36.4, 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0],
        ['Rib Roast', '1 lb.', 29.2, 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0],
        ['Chuck Roast', '1 lb.', 22.6, 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0],
        ['Plate', '1 lb.', 14.6, 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0],
        [
            'Liver (Beef)', '1 lb.', 26.8, 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8,
            316, 525
        ],
        ['Leg of Lamb', '1 lb.', 27.6, 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0],
        [
            'Lamb Chops (Rib)', '1 lb.', 36.6, 3.3, 140, 0.1, 15, 0, 1.7, 2.7,
            54, 0
        ],
        ['Pork Chops', '1 lb.', 30.7, 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0],
        [
            'Pork Loin Roast', '1 lb.', 24.2, 4.4, 249, 0.3, 37, 0, 18.2, 3.6,
            79, 0
        ],
        ['Bacon', '1 lb.', 25.6, 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0],
        ['Ham, smoked', '1 lb.', 27.4, 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0],
        ['Salt Pork', '1 lb.', 16, 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0],
        [
            'Roasting Chicken', '1 lb.', 30.3, 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8,
            68, 46
        ],
        ['Veal Cutlets', '1 lb.', 42.3, 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0],
        [
            'Salmon, Pink (can)', '16 oz.', 13, 5.8, 705, 6.8, 45, 3.5, 1, 4.9,
            209, 0
        ],
        ['Apples', '1 lb.', 4.4, 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544],
        ['Bananas', '1 lb.', 6.1, 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498],
        ['Lemons', '1 doz.', 26, 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952],
        ['Oranges', '1 doz.', 30.9, 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998],
        ['Green Beans', '1 lb.', 7.1, 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862],
        ['Cabbage', '1 lb.', 3.7, 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369],
        ['Carrots', '1 bunch', 4.7, 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608],
        ['Celery', '1 stalk', 7.3, 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313],
        ['Lettuce', '1 head', 8.2, 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449],
        ['Onions', '1 lb.', 3.6, 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184],
        [
            'Potatoes', '15 lb.', 34, 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198,
            2522
        ],
        ['Spinach', '1 lb.', 8.1, 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755],
        [
            'Sweet Potatoes', '1 lb.', 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4,
            83, 1912
        ],
        [
            'Peaches (can)', 'No. 2 1/2', 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5, 1,
            31, 196
        ],
        [
            'Pears (can)', 'No. 2 1/2', 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5,
            81
        ],
        [
            'Pineapple (can)', 'No. 2 1/2', 21.3, 2.4, 16, 0.4, 8, 2, 2.8, 0.8,
            7, 399
        ],
        [
            'Asparagus (can)', 'No. 2', 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1,
            17, 272
        ],
        [
            'Green Beans (can)', 'No. 2', 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3,
            32, 431
        ],
        [
            'Pork and Beans (can)', '16 oz.', 7.1, 7.5, 364, 4, 134, 3.5, 8.3,
            7.7, 56, 0
        ],
        ['Corn (can)', 'No. 2', 10.4, 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218],
        [
            'Peas (can)', 'No. 2', 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37,
            370
        ],
        [
            'Tomatoes (can)', 'No. 2', 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5,
            36, 1253
        ],
        [
            'Tomato Soup (can)', '10 1/2 oz.', 7.6, 1.6, 71, 0.6, 43, 57.9, 3.5,
            2.4, 67, 862
        ],
        [
            'Peaches, Dried', '1 lb.', 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3,
            55, 57
        ],
        [
            'Prunes, Dried', '1 lb.', 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65,
            257
        ],
        [
            'Raisins, Dried', '15 oz.', 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4,
            24, 136
        ],
        [
            'Peas, Dried', '1 lb.', 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4,
            162, 0
        ],
        [
            'Lima Beans, Dried', '1 lb.', 8.9, 17.4, 1055, 3.7, 459, 5.1, 26.9,
            38.2, 93, 0
        ],
        [
            'Navy Beans, Dried', '1 lb.', 5.9, 26.9, 1691, 11.4, 792, 0, 38.4,
            24.6, 217, 0
        ],
        ['Coffee', '1 lb.', 22.4, 0, 0, 0, 0, 0, 4, 5.1, 50, 0],
        ['Tea', '1/4 lb.', 17.4, 0, 0, 0, 0, 0, 0, 2.3, 42, 0],
        ['Cocoa', '8 oz.', 8.6, 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0],
        ['Chocolate', '8 oz.', 16.2, 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0],
        ['Sugar', '10 lb.', 51.7, 34.9, 0, 0, 0, 0, 0, 0, 0, 0],
        ['Corn Syrup', '24 oz.', 13.7, 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0],
        ['Molasses', '18 oz.', 13.6, 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0],
        [
            'Strawberry Preserves', '1 lb.', 20.5, 6.4, 11, 0.4, 7, 0.2, 0.2,
            0.4, 3, 0
        ],
    ]

    # Instantiate a Glop solver and naming it.
    solver = pywraplp.Solver('StiglerDietExample',
                             pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

    # Declare an array to hold our variables.
    foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]

    print('Number of variables =', solver.NumVariables())

    # Create the constraints, one per nutrient.
    constraints = []
    for i, nutrient in enumerate(nutrients):
        constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
        for j, item in enumerate(data):
            constraints[i].SetCoefficient(foods[j], item[i + 3])

    print('Number of constraints =', solver.NumConstraints())

    # Objective function: Minimize the sum of (price-normalized) foods.
    objective = solver.Objective()
    for food in foods:
        objective.SetCoefficient(food, 1)
    objective.SetMinimization()

    status = solver.Solve()

    # Check that the problem has an optimal solution.
    if status != solver.OPTIMAL:
        print('The problem does not have an optimal solution!')
        if status == solver.FEASIBLE:
            print('A potentially suboptimal solution was found.')
        else:
            print('The solver could not solve the problem.')
            exit(1)

    # Display the amounts (in dollars) to purchase of each food.
    nutrients_result = [0] * len(nutrients)
    print('\nAnnual Foods:')
    for i, food in enumerate(foods):
        if food.solution_value() > 0.0:
            print('{}: ${}'.format(data[i][0], 365. * food.solution_value()))
            for j, _ in enumerate(nutrients):
                nutrients_result[j] += data[i][j + 3] * food.solution_value()
    print('\nOptimal annual price: ${:.4f}'.format(365. * objective.Value()))

    print('\nNutrients per day:')
    for i, nutrient in enumerate(nutrients):
        print('{}: {:.2f} (min {})'.format(nutrient[0], nutrients_result[i],
                                           nutrient[1]))

    print('\nAdvanced usage:')
    print('Problem solved in ', solver.wall_time(), ' milliseconds')
    print('Problem solved in ', solver.iterations(), ' iterations')


if __name__ == '__main__':
    main()

C++

// The Stigler diet problem.
#include <array>
#include <string>
#include <utility>  // std::pair
#include <vector>

#include "absl/flags/flag.h"
#include "absl/flags/parse.h"
#include "absl/flags/usage.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.h"

namespace operations_research {
void StiglerDiet() {
  // Nutrient minimums.
  const std::vector<std::pair<std::string, double>> nutrients = {
      {"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
      {"Calcium (g)", 0.8},     {"Iron (mg)", 12.0},
      {"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
      {"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
      {"Vitamin C (mg)", 75.0}};

  struct Commodity {
    std::string name;  //!< Commodity name
    std::string unit;  //!< Unit
    double price;      //!< 1939 price per unit (cents)
    //! Calories (kcal),
    //! Protein (g),
    //! Calcium (g),
    //! Iron (mg),
    //! Vitamin A (kIU),
    //! Vitamin B1 (mg),
    //! Vitamin B2 (mg),
    //! Niacin (mg),
    //! Vitamin C (mg)
    std::array<double, 9> nutrients;
  };

  std::vector<Commodity> data = {
      {"Wheat Flour (Enriched)",
       "10 lb.",
       36,
       {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}},
      {"Macaroni", "1 lb.", 14.1, {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}},
      {"Wheat Cereal (Enriched)",
       "28 oz.",
       24.2,
       {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}},
      {"Corn Flakes", "8 oz.", 7.1, {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}},
      {"Corn Meal",
       "1 lb.",
       4.6,
       {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}},
      {"Hominy Grits",
       "24 oz.",
       8.5,
       {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}},
      {"Rice", "1 lb.", 7.5, {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}},
      {"Rolled Oats", "1 lb.", 7.1, {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}},
      {"White Bread (Enriched)",
       "1 lb.",
       7.9,
       {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}},
      {"Whole Wheat Bread",
       "1 lb.",
       9.1,
       {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}},
      {"Rye Bread", "1 lb.", 9.1, {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}},
      {"Pound Cake", "1 lb.", 24.8, {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}},
      {"Soda Crackers", "1 lb.", 15.1, {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}},
      {"Milk", "1 qt.", 11, {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}},
      {"Evaporated Milk (can)",
       "14.5 oz.",
       6.7,
       {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}},
      {"Butter", "1 lb.", 30.8, {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}},
      {"Oleomargarine", "1 lb.", 16.1, {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}},
      {"Eggs", "1 doz.", 32.6, {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}},
      {"Cheese (Cheddar)",
       "1 lb.",
       24.2,
       {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}},
      {"Cream", "1/2 pt.", 14.1, {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}},
      {"Peanut Butter",
       "1 lb.",
       17.9,
       {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}},
      {"Mayonnaise", "1/2 pt.", 16.7, {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}},
      {"Crisco", "1 lb.", 20.3, {20.1, 0, 0, 0, 0, 0, 0, 0, 0}},
      {"Lard", "1 lb.", 9.8, {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}},
      {"Sirloin Steak",
       "1 lb.",
       39.6,
       {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}},
      {"Round Steak", "1 lb.", 36.4, {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}},
      {"Rib Roast", "1 lb.", 29.2, {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}},
      {"Chuck Roast", "1 lb.", 22.6, {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}},
      {"Plate", "1 lb.", 14.6, {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}},
      {"Liver (Beef)",
       "1 lb.",
       26.8,
       {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}},
      {"Leg of Lamb", "1 lb.", 27.6, {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}},
      {"Lamb Chops (Rib)",
       "1 lb.",
       36.6,
       {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}},
      {"Pork Chops", "1 lb.", 30.7, {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}},
      {"Pork Loin Roast",
       "1 lb.",
       24.2,
       {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}},
      {"Bacon", "1 lb.", 25.6, {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}},
      {"Ham, smoked", "1 lb.", 27.4, {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}},
      {"Salt Pork", "1 lb.", 16, {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}},
      {"Roasting Chicken",
       "1 lb.",
       30.3,
       {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}},
      {"Veal Cutlets", "1 lb.", 42.3, {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}},
      {"Salmon, Pink (can)",
       "16 oz.",
       13,
       {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}},
      {"Apples", "1 lb.", 4.4, {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}},
      {"Bananas", "1 lb.", 6.1, {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}},
      {"Lemons", "1 doz.", 26, {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}},
      {"Oranges", "1 doz.", 30.9, {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}},
      {"Green Beans", "1 lb.", 7.1, {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}},
      {"Cabbage", "1 lb.", 3.7, {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}},
      {"Carrots", "1 bunch", 4.7, {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}},
      {"Celery", "1 stalk", 7.3, {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}},
      {"Lettuce", "1 head", 8.2, {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}},
      {"Onions", "1 lb.", 3.6, {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}},
      {"Potatoes",
       "15 lb.",
       34,
       {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}},
      {"Spinach", "1 lb.", 8.1, {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}},
      {"Sweet Potatoes",
       "1 lb.",
       5.1,
       {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}},
      {"Peaches (can)",
       "No. 2 1/2",
       16.8,
       {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}},
      {"Pears (can)",
       "No. 2 1/2",
       20.4,
       {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}},
      {"Pineapple (can)",
       "No. 2 1/2",
       21.3,
       {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}},
      {"Asparagus (can)",
       "No. 2",
       27.7,
       {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}},
      {"Green Beans (can)",
       "No. 2",
       10,
       {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}},
      {"Pork and Beans (can)",
       "16 oz.",
       7.1,
       {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}},
      {"Corn (can)", "No. 2", 10.4, {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}},
      {"Peas (can)",
       "No. 2",
       13.8,
       {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}},
      {"Tomatoes (can)",
       "No. 2",
       8.6,
       {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}},
      {"Tomato Soup (can)",
       "10 1/2 oz.",
       7.6,
       {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}},
      {"Peaches, Dried",
       "1 lb.",
       15.7,
       {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}},
      {"Prunes, Dried",
       "1 lb.",
       9,
       {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}},
      {"Raisins, Dried",
       "15 oz.",
       9.4,
       {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}},
      {"Peas, Dried",
       "1 lb.",
       7.9,
       {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}},
      {"Lima Beans, Dried",
       "1 lb.",
       8.9,
       {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}},
      {"Navy Beans, Dried",
       "1 lb.",
       5.9,
       {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}},
      {"Coffee", "1 lb.", 22.4, {0, 0, 0, 0, 0, 4, 5.1, 50, 0}},
      {"Tea", "1/4 lb.", 17.4, {0, 0, 0, 0, 0, 0, 2.3, 42, 0}},
      {"Cocoa", "8 oz.", 8.6, {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}},
      {"Chocolate", "8 oz.", 16.2, {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}},
      {"Sugar", "10 lb.", 51.7, {34.9, 0, 0, 0, 0, 0, 0, 0, 0}},
      {"Corn Syrup", "24 oz.", 13.7, {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}},
      {"Molasses", "18 oz.", 13.6, {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}},
      {"Strawberry Preserves",
       "1 lb.",
       20.5,
       {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}}};

  // Create the linear solver with the GLOP backend.
  std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));

  std::vector<MPVariable*> foods;
  const double infinity = solver->infinity();
  for (const Commodity& commodity : data) {
    foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
  }
  LOG(INFO) << "Number of variables = " << solver->NumVariables();

  // Create the constraints, one per nutrient.
  std::vector<MPConstraint*> constraints;
  for (std::size_t i = 0; i < nutrients.size(); ++i) {
    constraints.push_back(
        solver->MakeRowConstraint(nutrients[i].second, infinity));
    for (std::size_t j = 0; j < data.size(); ++j) {
      constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
    }
  }
  LOG(INFO) << "Number of constraints = " << solver->NumConstraints();

  MPObjective* const objective = solver->MutableObjective();
  for (size_t i = 0; i < data.size(); ++i) {
    objective->SetCoefficient(foods[i], 1);
  }
  objective->SetMinimization();

  const MPSolver::ResultStatus result_status = solver->Solve();

  // Check that the problem has an optimal solution.
  if (result_status != MPSolver::OPTIMAL) {
    LOG(INFO) << "The problem does not have an optimal solution!";
    if (result_status == MPSolver::FEASIBLE) {
      LOG(INFO) << "A potentially suboptimal solution was found";
    } else {
      LOG(INFO) << "The solver could not solve the problem.";
      return;
    }
  }

  std::vector<double> nutrients_result(nutrients.size());
  LOG(INFO) << "";
  LOG(INFO) << "Annual Foods:";
  for (std::size_t i = 0; i < data.size(); ++i) {
    if (foods[i]->solution_value() > 0.0) {
      LOG(INFO) << data[i].name << ": $"
                << std::to_string(365. * foods[i]->solution_value());
      for (std::size_t j = 0; j < nutrients.size(); ++j) {
        nutrients_result[j] +=
            data[i].nutrients[j] * foods[i]->solution_value();
      }
    }
  }
  LOG(INFO) << "";
  LOG(INFO) << "Optimal annual price: $"
            << std::to_string(365. * objective->Value());
  LOG(INFO) << "";
  LOG(INFO) << "Nutrients per day:";
  for (std::size_t i = 0; i < nutrients.size(); ++i) {
    LOG(INFO) << nutrients[i].first << ": "
              << std::to_string(nutrients_result[i]) << " (min "
              << std::to_string(nutrients[i].second) << ")";
  }

  LOG(INFO) << "";
  LOG(INFO) << "Advanced usage:";
  LOG(INFO) << "Problem solved in " << solver->wall_time() << " milliseconds";
  LOG(INFO) << "Problem solved in " << solver->iterations() << " iterations";
}
}  // namespace operations_research

int main(int argc, char** argv) {
  google::InitGoogleLogging(argv[0]);
  absl::ParseCommandLine(argc, argv);
  absl::SetFlag(&FLAGS_logtostderr, true);
  operations_research::StiglerDiet();
  return EXIT_SUCCESS;
}

Java

// The Stigler diet problem.
package com.google.ortools.linearsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.util.ArrayList;
import java.util.List;

/** Stigler diet example. */
public final class StiglerDiet {
  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Nutrient minimums.
    List<Object[]> nutrients = new ArrayList<>();
    nutrients.add(new Object[] {"Calories (kcal)", 3.0});
    nutrients.add(new Object[] {"Protein (g)", 70.0});
    nutrients.add(new Object[] {"Calcium (g)", 0.8});
    nutrients.add(new Object[] {"Iron (mg)", 12.0});
    nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
    nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
    nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
    nutrients.add(new Object[] {"Niacin (mg)", 18.0});
    nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});

    List<Object[]> data = new ArrayList<>();
    data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
        new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
    data.add(new Object[] {
        "Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
    data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
        new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
    data.add(new Object[] {
        "Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
    data.add(new Object[] {
        "Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
    data.add(new Object[] {
        "Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
    data.add(
        new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
    data.add(new Object[] {
        "Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
    data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
        new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
    data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
        new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
    data.add(new Object[] {
        "Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
    data.add(new Object[] {
        "Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
    data.add(new Object[] {
        "Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
    data.add(
        new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
    data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
        new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
    data.add(
        new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
    data.add(new Object[] {
        "Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
    data.add(new Object[] {
        "Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
    data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
        new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
    data.add(new Object[] {
        "Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
    data.add(new Object[] {
        "Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
    data.add(new Object[] {
        "Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
    data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
    data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
    data.add(new Object[] {
        "Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
    data.add(new Object[] {
        "Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
    data.add(
        new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
    data.add(new Object[] {
        "Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
    data.add(
        new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
    data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
        new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
    data.add(new Object[] {
        "Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
    data.add(new Object[] {
        "Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
    data.add(new Object[] {
        "Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
    data.add(new Object[] {
        "Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
    data.add(new Object[] {
        "Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
    data.add(new Object[] {
        "Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
    data.add(new Object[] {
        "Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
    data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
        new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
    data.add(new Object[] {
        "Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
    data.add(new Object[] {
        "Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
    data.add(new Object[] {
        "Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
    data.add(new Object[] {
        "Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
    data.add(
        new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
    data.add(new Object[] {
        "Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
    data.add(new Object[] {
        "Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
    data.add(new Object[] {
        "Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
    data.add(new Object[] {
        "Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
    data.add(new Object[] {
        "Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
    data.add(new Object[] {
        "Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
    data.add(new Object[] {
        "Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
    data.add(new Object[] {
        "Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
    data.add(new Object[] {
        "Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
    data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
        new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
    data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
        new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
    data.add(new Object[] {
        "Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
    data.add(new Object[] {
        "Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
    data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
        new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
    data.add(new Object[] {
        "Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
    data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
        new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
    data.add(new Object[] {
        "Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
    data.add(new Object[] {
        "Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
    data.add(new Object[] {
        "Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
    data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
        new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
    data.add(new Object[] {
        "Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
    data.add(new Object[] {
        "Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
    data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
        new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
    data.add(new Object[] {
        "Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
    data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
        new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
    data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
        new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
    data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
    data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
    data.add(
        new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
    data.add(new Object[] {
        "Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
    data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
    data.add(new Object[] {
        "Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
    data.add(new Object[] {
        "Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
    data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
        new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});


    // Create the linear solver with the GLOP backend.
    MPSolver solver = MPSolver.createSolver("GLOP");
    if (solver == null) {
      System.out.println("Could not create solver GLOP");
      return;
    }

    double infinity = java.lang.Double.POSITIVE_INFINITY;
    List<MPVariable> foods = new ArrayList<>();
    for (int i = 0; i < data.size(); ++i) {
      foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
    }
    System.out.println("Number of variables = " + solver.numVariables());

    MPConstraint[] constraints = new MPConstraint[nutrients.size()];
    for (int i = 0; i < nutrients.size(); ++i) {
      constraints[i] = solver.makeConstraint(
          (double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
      for (int j = 0; j < data.size(); ++j) {
        constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
      }
      // constraints.add(constraint);
    }
    System.out.println("Number of constraints = " + solver.numConstraints());

    MPObjective objective = solver.objective();
    for (int i = 0; i < data.size(); ++i) {
      objective.setCoefficient(foods.get(i), 1);
    }
    objective.setMinimization();

    final MPSolver.ResultStatus resultStatus = solver.solve();

    // Check that the problem has an optimal solution.
    if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
      System.err.println("The problem does not have an optimal solution!");
      if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
        System.err.println("A potentially suboptimal solution was found.");
      } else {
        System.err.println("The solver could not solve the problem.");
        return;
      }
    }

    // Display the amounts (in dollars) to purchase of each food.
    double[] nutrientsResult = new double[nutrients.size()];
    System.out.println("\nAnnual Foods:");
    for (int i = 0; i < foods.size(); ++i) {
      if (foods.get(i).solutionValue() > 0.0) {
        System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
        for (int j = 0; j < nutrients.size(); ++j) {
          nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
        }
      }
    }
    System.out.println("\nOptimal annual price: $" + 365 * objective.value());

    System.out.println("\nNutrients per day:");
    for (int i = 0; i < nutrients.size(); ++i) {
      System.out.println(
          nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
    }

    System.out.println("\nAdvanced usage:");
    System.out.println("Problem solved in " + solver.wallTime() + " milliseconds");
    System.out.println("Problem solved in " + solver.iterations() + " iterations");
  }

  private StiglerDiet() {}
}

C#

// The Stigler diet problem.
using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;

public class StiglerDiet
{
    static void Main()
    {
        // Nutrient minimums.
        (String Name, double Value)[] nutrients =
            new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0),    ("Calcium (g)", 0.8),
                    ("Iron (mg)", 12.0),      ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
                    ("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0),    ("Vitamin C (mg)", 75.0) };

        (String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
            ("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
            ("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
            ("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
            ("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
            ("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
            ("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
            ("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
            ("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
            ("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
            ("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
            ("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
            ("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
            ("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
            ("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
            ("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
            ("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
            ("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
            ("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
            ("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
            ("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
            ("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
            ("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
            ("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
            ("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
            ("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
            ("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
            ("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
            ("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
            ("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
            ("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
            ("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
            ("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
            ("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
            ("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
            ("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
            ("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
            ("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
            ("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
            ("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
            ("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
            ("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
            ("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
            ("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
            ("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
            ("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
            ("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
            ("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
            ("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
            ("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
            ("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
            ("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
            ("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
            ("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
            ("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
            ("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
            ("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
            ("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
            ("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
            ("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
            ("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
            ("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
            ("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
            ("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
            ("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
            ("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
            ("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
            ("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
            ("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
            ("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
            ("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
            ("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
            ("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
            ("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
            ("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
            ("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
        };

        // Create the linear solver with the GLOP backend.
        Solver solver = Solver.CreateSolver("GLOP");

        List<Variable> foods = new List<Variable>();
        for (int i = 0; i < data.Length; ++i)
        {
            foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
        }
        Console.WriteLine($"Number of variables = {solver.NumVariables()}");

        List<Constraint> constraints = new List<Constraint>();
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Constraint constraint =
                solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
            for (int j = 0; j < data.Length; ++j)
            {
                constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
            }
            constraints.Add(constraint);
        }
        Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");

        Objective objective = solver.Objective();
        for (int i = 0; i < data.Length; ++i)
        {
            objective.SetCoefficient(foods[i], 1);
        }
        objective.SetMinimization();

        Solver.ResultStatus resultStatus = solver.Solve();

        // Check that the problem has an optimal solution.
        if (resultStatus != Solver.ResultStatus.OPTIMAL)
        {
            Console.WriteLine("The problem does not have an optimal solution!");
            if (resultStatus == Solver.ResultStatus.FEASIBLE)
            {
                Console.WriteLine("A potentially suboptimal solution was found.");
            }
            else
            {
                Console.WriteLine("The solver could not solve the problem.");
                return;
            }
        }

        // Display the amounts (in dollars) to purchase of each food.
        double[] nutrientsResult = new double[nutrients.Length];
        Console.WriteLine("\nAnnual Foods:");
        for (int i = 0; i < foods.Count; ++i)
        {
            if (foods[i].SolutionValue() > 0.0)
            {
                Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
                for (int j = 0; j < nutrients.Length; ++j)
                {
                    nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
                }
            }
        }
        Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");

        Console.WriteLine("\nNutrients per day:");
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
        }

        Console.WriteLine("\nAdvanced usage:");
        Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
        Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
    }
}