2. (a) Suppose we are given a linear program in standard equation form maximize cx subject to Ax = b, x ≥ 0. Given two different optimal solutions y and z to this linear program, prove that every convex combination of y and z is also an optimal solution of the program. (b) Briefly explain how to use part (a) to show that every linear program has either 0, 1, or infinitely many optimal solutions.

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