A basic property of any linear programming problem with a bounded feasible region is that every feasible solution can be expressed as a convex combination of the CPF solutions. Similarly, for the augmented form of the problem, every feasible solution can be expressed as a convex combination of the BF solutions. If there is only one CPF solution with the optimal objective function value for the linear programming problem, show that the objective function value for every convex combination of BF solutions must be worse than the optimal solution.