Solving the problem consists of finding a value for each variable that satisfies the constraints and maximizes the objective containing the relaxed constraints.

Add the following code after the comment //Create an instance of IloSolver

    IloSolver solver(model);

You now use the member function IloSolver::solve, which solves a problem by using a default goal to launch the search.

Add the following code after the comment //Search for a solution

    if (solver.solve())

You use the member functions and streams IloAlgorithm::getStatus, IloSolver::getValue, and the function print to display the solution. These are already provided for you in the exercise code.

      {
      solver.out() << solver.getStatus() << " Solution" << endl;
      solver.out() << "Objective = " << solver.getValue(obj) << endl;
      print(solver, "Belgium:     ", Belgium);
      print(solver, "Denmark:     ", Denmark);
      print(solver, "France:      ", France);
      print(solver, "Germany:     ", Germany);
      print(solver, "Netherlands: ", Netherlands);
      print(solver, "Luxembourg:  ", Luxembourg);
    }

Compile and run the program. You should get the following results:

Optimal Solution
Objective = 9611
Belgium:     white
Denmark:     blue
France:      blue
Germany:     yellow
Netherlands: blue
Luxembourg:  blue

As you can see, only three colors are used. The "unrelaxed" constraints are all satisfied. The objective is maximized. The relaxed constraint Luxembourg != Germany is satisfied. This adds 9043 to the expression. The relaxed constraint Luxembourg != Belgium is also satisfied. This adds 568 to the expression. This gives a value of 9611 to the objective. The only way that the value of this objective expression could be greater would be if the relaxed constraint Luxembourg != France were also satisfied. However, this is not a possible solution since it would mean that "unrelaxed" constraints would not be satisfied.