# Question: A basic property of any linear programming problem with a

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 (perhaps in more than one way). Similarly, for the augmented form of the problem, every feasible solution can be expressed as a convex combination of the BF solutions.

(a) Show that any convex combination of any set of feasible solutions must be a feasible solution (so that any convex combination of CPF solutions must be feasible).

(b) Use the result quoted in part (a) to show that any convex combination of BF solutions must be a feasible solution.

(a) Show that any convex combination of any set of feasible solutions must be a feasible solution (so that any convex combination of CPF solutions must be feasible).

(b) Use the result quoted in part (a) to show that any convex combination of BF solutions must be a feasible solution.

## Answer to relevant Questions

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 ...Consider the following problem. Minimize Z = 2x1 +3x2 + x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Reformulate this problem to fit our standard form for a linear programming model presented in Sec. 3.2. (b) Using ...Consider the following problem. Minimize Z = 3x1 + 2x2 + 4x3, 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 the problem. (b) Using the ...Consider the following problem. Maximize Z = – 2x1 + x2 – 4x3 + 3x4, Subject to and x2 ≥ 0, x3 0, x4 ≥ 0 (no nonnegativity constraint for x1). (a) Reformulate this problem to fit our standard form for a linear ...Describe graphically what the simplex method does step by step to solve the following problem. Maximize Z = 2x1 + 3x2, Subject to and x1 ≥ 0, x2 ≥ 0.Post your question