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`


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

// Add variables, constraints and define the objective using 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(`Value of x: ${solution.getVariableValue('x')}`);
  Logger.log(`Value of y: ${solution.getVariableValue('y')}`);
}
```

### Properties

| Property | Type | Description |
|---|---|---|
| `Status` | `https://developers.google.com/apps-script/reference/optimization/status` | Status of the solver. |
| `VariableType` | `https://developers.google.com/apps-script/reference/optimization/variable-type` | Type of variables created by the solver. |

### Methods

| Method | Return type | Brief description |
|---|---|---|
| `https://developers.google.com/apps-script/reference/optimization/linear-optimization-service#createEngine()` | `https://developers.google.com/apps-script/reference/optimization/linear-optimization-engine` | 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).

```javascript
// Creates a linear optimization engine.
const engine = LinearOptimizationService.createEngine();
engine.addVariable('x', 0, 10);

// ...
```

#### Return


`https://developers.google.com/apps-script/reference/optimization/linear-optimization-engine` --- a linear optimization engine