LinearOptimizationSolution

The solution of a linear program. The example below solves the following linear program:

Two variables, `x` and `y`:  


`0 ≤ x ≤ 10`


`0 ≤ y ≤ 5`


Constraints:  


`0 ≤ 2 * x + 5 * y ≤ 10`


`0 ≤ 10 * x + 3 * y ≤ 20`


Objective:  

Maximize `x + y`


```javascript
const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc. Add two variables, 0 <= x <= 10 and 0 <= y <= 5
engine.addVariable('x', 0, 10);
engine.addVariable('y', 0, 5);

// Create the constraint: 0 <= 2 * x + 5 * y <= 10
let constraint = engine.addConstraint(0, 10);
constraint.setCoefficient('x', 2);
constraint.setCoefficient('y', 5);

// Create the constraint: 0 <= 10 * x + 3 * y <= 20
constraint = engine.addConstraint(0, 20);
constraint.setCoefficient('x', 10);
constraint.setCoefficient('y', 3);

// Set the objective to be x + y
engine.setObjectiveCoefficient('x', 1);
engine.setObjectiveCoefficient('y', 1);

// Engine should maximize the objective
engine.setMaximization();

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  Logger.log(`No solution ${solution.getStatus()}`);
} else {
  Logger.log(`Objective  value: ${solution.getObjectiveValue()}`);
  Logger.log(`Value of x: ${solution.getVariableValue('x')}`);
  Logger.log(`Value of y: ${solution.getVariableValue('y')}`);
}
```

### Methods

| Method | Return type | Brief description |
|---|---|---|
| `https://developers.google.com/apps-script/reference/optimization/linear-optimization-solution#getObjectiveValue()` | `Number` | Gets the value of the objective function in the current solution. |
| `https://developers.google.com/apps-script/reference/optimization/linear-optimization-solution#getStatus()` | `https://developers.google.com/apps-script/reference/optimization/status` | Gets the status of the solution. |
| `https://developers.google.com/apps-script/reference/optimization/linear-optimization-solution#getVariableValue(String)` | `Number` | Gets the value of a variable in the solution created by the last call to `https://developers.google.com/apps-script/reference/optimization/linear-optimization-engine#solve()`. |
| `https://developers.google.com/apps-script/reference/optimization/linear-optimization-solution#isValid()` | `Boolean` | Determines whether the solution is either feasible or optimal. |

## Detailed documentation

### `getObjectiveValue()`

Gets the value of the objective function in the current solution.

```javascript
const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
Logger.log(`ObjectiveValue: ${solution.getObjectiveValue()}`);
```

#### Return


`Number` --- the value of the objective function

*** ** * ** ***

### `getStatus()`

Gets the status of the solution. Before solving a problem, the status will be `NOT_SOLVED`.

```javascript
const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
const status = solution.getStatus();

if (status !== LinearOptimizationService.Status.FEASIBLE &&
    status !== LinearOptimizationService.Status.OPTIMAL) {
  throw `No solution ${status}`;
}
Logger.log(`Status: ${status}`);
```

#### Return


`https://developers.google.com/apps-script/reference/optimization/status` --- the status of the solver

*** ** * ** ***

### `getVariableValue(variableName)`

Gets the value of a variable in the solution created by the last call to `https://developers.google.com/apps-script/reference/optimization/linear-optimization-engine#solve()`.

```javascript
const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
Logger.log(`Value of x: ${solution.getVariableValue('x')}`);
```

#### Parameters

| Name | Type | Description |
|---|---|---|
| `variableName` | `String` | name of the variable |

#### Return


`Number` --- the value of the variable in the solution

*** ** * ** ***

### `isValid()`

Determines whether the solution is either feasible or optimal.

```javascript
const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  throw `No solution ${solution.getStatus()}`;
}
```

#### Return


`Boolean` --- `true` if the solution is valid (`https://developers.google.com/apps-script/reference/optimization/status#FEASIBLE` or
`https://developers.google.com/apps-script/reference/optimization/status#OPTIMAL`); `false` if not