onsider the problem min max (a;x -b;) i=1,....m s.t. rER. t v be the optimal value of the above optimization problem, let A be the m x n matrix whose rows e al,...,a", and let b be the vector whose components are b1, ..., bm. 1) (7 points) Consider any vector p E R" such that p'A = 0', p 2 0, and _ _p; = 1. Show that -p'b c v. ) (3 points) In order to obtain the best possible lower bound of the form obtained in part (a), we consider the linear program max - p'b s.t. p'A = 0' pi = 1 i-1