# Class LinearOptimizationService

LinearOptimizationService

The linear optimization service, used to model and solve linear and mixed-integer linear programs. 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`

```var engine = LinearOptimizationService.createEngine();

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

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

// Create the constraint: 0 <= 10 * x + 3 * y <= 20
var 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
var solution = engine.solve();
if (!solution.isValid()) {
Logger.log('No solution ' + solution.getStatus());
} else {
Logger.log('Value of x: ' + solution.getVariableValue('x'));
Logger.log('Value of y: ' + solution.getVariableValue('y'));
}```

### Properties

PropertyTypeDescription
`Status``Status`Status of the solver.
`VariableType``VariableType`Type of variables created by the solver.

### Methods

MethodReturn typeBrief description
`createEngine()``LinearOptimizationEngine`Creates an engine to to solve linear programs (potentially mixed-integer programs).

## Detailed documentation

### `createEngine()`

Creates an engine to to solve linear programs (potentially mixed-integer programs).

```// Creates a linear optimization engine.
var engine = LinearOptimizationService.createEngine();
`LinearOptimizationEngine` — a linear optimization engine