Adding Constraints in Google Apps Script Linear Optimization Service

I need to solve an assignment problem with Google Apps Script. The LinearOptimizationService seemed to be promising so what I tried is to port a corresponding example from the google or-tools .

Unfortunately, I couldn't find out a way how I set up the constraint that each worker is assigned to exactly one task.

The working code (without the constraint) is as follows:

function myFunction() {
  // Create the variables
  var engine = LinearOptimizationService.createEngine();
  
  const costMatrix = [[7,5,4,8,3]
                     ,[2,5,6,7,1]
                     ,[2,8,9,5,2]
                     ,[2,5,6,7,1]
                     ,[2,8,1,5,9]]

  const capacities = [1,1,1,1,1]

  // initialize the decision variables
  x = new Array(costMatrix.length);
  for (let i=0; i<costMatrix.length; i++){
    x[i] = new Array(costMatrix[0].length);
    for (let j=0; j<costMatrix[0].length; j++){
      x[i][j] = engine.addVariable(`x${i}${j}`, 0, 1, LinearOptimizationService.VariableType.INTEGER);
    }
  }

  // Each worker is assigned to at most one task.
  for (let i = 0; i < costMatrix.length; ++i) {
    constraint = engine.addConstraint(0, 1);
    for (let j = 0; j < costMatrix[0].length; ++j) {
      constraint.setCoefficient(`x${i}${j}`, 1);
    }
  }

  // Each task is assigned to exactly one worker.
  for (let j = 0; j < costMatrix[0].length; ++j) {
    constraint = engine.addConstraint(1, 1);
    for (let i = 0; i < costMatrix.length; ++i) {
      constraint.setCoefficient(`x${i}${j}`, 1);
    }
  }

  for (let i = 0; i < costMatrix.length; ++i) {
    for (let j = 0; j < costMatrix[0].length; ++j) {
      engine.setObjectiveCoefficient(`x${i}${j}`, costMatrix[i][j]);
    }
  }

  engine.setMinimization()

  // Solve the linear program
  var solution = engine.solve(30);
  if (!solution.isValid()) {
    throw 'No solution ' + solution.getStatus();
  }
  Logger.log('ObjectiveValue: ' + solution.getObjectiveValue());
  for (let i=0; i<costMatrix.length; i++){
    for (let j=0; j<costMatrix[0].length; j++){
      Logger.log(`Value of: x${i}${j} ` + solution.getVariableValue(`x${i}${j}`));
    }
  }
}

Any help is appreciated.

Thanks