# Class LinearOptimizationSolution

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`

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

// Add variables, constraints and define the objective with 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('Objective  value: ' + solution.getObjectiveValue());
Logger.log('Value of x: ' + solution.getVariableValue('x'));
Logger.log('Value of y: ' + solution.getVariableValue('y'));
}```

### Methods

MethodReturn typeBrief description
`getObjectiveValue()``Number`Gets the value of the objective function in the current solution.
`getStatus()``Status`Gets the status of the solution.
`getVariableValue(variableName)``Number`Gets the value of a variable in the solution created by the last call to `LinearOptimizationEngine.solve()`.
`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.

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

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc

// ...

// Solve the linear program
var 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`.

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

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc

// ...

// Solve the linear program
var solution = engine.solve();
if (solution.getStatus() != LinearOptimizationService.Status.FEASIBLE &&
solution.getStatus() != LinearOptimizationService.Status.OPTIMAL) {
throw 'No solution ' + status;
}
Logger.log('Status: ' + solution.getStatus());```

#### Return

`Status` — the status of the solver

### `getVariableValue(variableName)`

Gets the value of a variable in the solution created by the last call to `LinearOptimizationEngine.solve()`.

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

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc

// ...

// Solve the linear program
var solution = engine.solve();
Logger.log('Value of x: ' + solution.getVariableValue('x'));```

#### Parameters

NameTypeDescription
`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.

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

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc
`Boolean``true` if the solution is valid (`Status.FEASIBLE` or `Status.OPTIMAL`); `false` if not