Create and Solve Maximization Problem

Create a linear programming problem for maximization. The problem has two positive variables and three linear inequality constraints.

prob = optimproblem('ObjectiveSense','max');

Create positive variables. Include an objective function in the problem.

x = optimvar('x',2,1,'LowerBound',0);
prob.Objective = x(1) + 2*x(2);

Create linear inequality constraints in the problem.

cons1 = x(1) + 5*x(2) <= 100;
cons2 = x(1) + x(2) <= 40;
cons3 = 2*x(1) + x(2)/2 <= 60;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;

Review the problem.

showproblem(prob)

  OptimizationProblem : 

	max :
       x(1, 1) + 2*x(2, 1)

	subject to cons1:
       x(1, 1) + 5*x(2, 1) <= 100

	subject to cons2:
       x(1, 1) + x(2, 1) <= 40

	subject to cons3:
       2*x(1, 1) + 0.5*x(2, 1) <= 60

	variable bounds:
       0 <= x(1, 1)
       0 <= x(2, 1)

Solve the problem.

sol = solve(prob);
sol.x

Optimal solution found.


ans =

   25.0000
   15.0000