Parametric LPs, B.T. 5.14, pg 228

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Problem # 2 ( Parametric LP's , B . T. 5.14 , pg 228 ) Consider the problem min ( C + Ad ) To Ar = 6 + Of I DO where A is an mix in matrix with linearly independent rows . We assume that the problem is feasible and the optimal cost f ( 1 ) is finite for all values of A in some interval Or , Oz 1 . Suppose that a certain basis is optimal for A 10 and for A O . Prove that the same basis is optimal for o - 5 2 . Show that f is a piecewise quadratic function of 6 . Give an upper bound on the number of " pieces 3 . Let b = 0 and c - O . Suppose that a certain basis is optimal for A = 1 . For what other nonnegative values of A is that same basis optimal ? Is f (9 ) convex , concave , or neither