# Question: Using the facts given in Prob 4 5 5 show that the

Using the facts given in Prob. 4.5-5, show that the following statements must be true for any linear programming problem that has a bounded feasible region and multiple optimal solutions:

(a) Every convex combination of the optimal BF solutions must be optimal.

(b) No other feasible solution can be optimal.

(a) Every convex combination of the optimal BF solutions must be optimal.

(b) No other feasible solution can be optimal.

## Answer to relevant Questions

Consider a two-variable linear programming problem whose CPF solutions are (0, 0), (6, 0), (6, 3), (3, 3), and (0, 2). (See Prob. 3.2-2 for a graph of the feasible region.) (a) Use the graph of the feasible region to ...For the Big M method, explain why the simplex method never would choose an artificial variable to be an entering basic variable once all the artificial variables are nonbasic. Follow the instructions of Prob. 4.6-9 for the following problem. Minimize Z = 3x1 + 2x2 + 7x3 Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Using the Big M method, work through the simplex method step by step to solve ...Consider the following problem. Maximize Z = 4x1 + 5x2 + 3x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Repeat Prob. 4.9-1 for the model in Prob. 4.1-5. Repeat Prob.Post your question