Use what you have learned in this lesson to model and solve the following problem. You are the manager of a coffee shop. You sell a house blend that is composed of the following five types of coffee: Costa Rican (cost per unit is $2), Hawaiian (cost per unit $5), Jamaican (cost per unit $3), Kenyan (cost per unit $9), and Nicaraguan (cost per unit $4). You need to make a batch of the house blend. In this batch, you must use at least 2 units of each type of coffee. You can use no more than 3 units of the Costa Rican coffee, no more than 3 units of the Jamaican coffee, and no more than 4 units of the Kenyan coffee. You want the total cost for the batch of house blend to be equal to $100. Write a natural language description of this problem and then model and solve it.

Suggested Answer

Describe

Model

Solve

The complete program follows. You can also view it online in the file YourSolverHome/examples/src/money_ex4.cpp.

#include <ilsolver/ilosolverint.h>
ILOSTLBEGIN
 
int main() {
  IloEnv env;
  try {
    IloModel model(env);
    IloInt nCoffee = 5, Sum = 100;
    IloIntArray coeffs(env, nCoffee, 2, 5, 3, 9, 4);
    env.out() << coeffs << endl;
    IloIntVarArray units(env, nCoffee, 0, Sum);
    model.add(units[0] >= 2);
    model.add(units[1] >= 2);
    model.add(units[2] >= 2);
    model.add(units[3] >= 2);
    model.add(units[4] >= 2);
    model.add(units[0] <= 3);
    model.add(units[2] <= 3);
    model.add(units[4] <= 4);
    model.add(IloScalProd(units, coeffs) == Sum);
    IloSolver solver(model);
    solver.startNewSearch();
    IloInt solutionCounter = 0;
    while(solver.next()) {
      solver.out() << "solution  " << ++solutionCounter << ":\t";
      for (IloInt i = 0; i < nCoffee; i++)
        solver.out() << solver.getValue(units[i]) << " ";
      solver.out() << endl;
    }
    solver.endSearch();
  }
  catch (IloException& ex) {
    cout << "Error: " << ex << endl;
  }
  env.end();
  return 0;
}
 

Results

[2, 5, 3, 9, 4]
solution 1:     2 2 2 8 2
solution 2:     2 3 2 7 3
solution 3:     2 4 2 6 4
solution 4:     2 5 3 6 2
solution 5:     2 6 3 5 3
solution 6:     2 7 3 4 4
solution 7:     2 11 2 3 2
solution 8:     2 12 2 2 3
solution 9:     3 2 3 7 3
solution 10:    3 3 3 6 4
solution 11:    3 7 2 5 2
solution 12:    3 8 2 4 3
solution 13:    3 9 2 3 4
solution 14:    3 10 3 3 2
solution 15:    3 11 3 2 3