# A basic property of any linear programming problem witha 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.

1. A basic property of any linear programming problem witha 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).

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

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