'5 Consider the LP (P) below, on optimization variables a: = ($1, . . . ,3\"). max. c - a: s.t. Am 5 b a: 2 0 Now consider the following LP (Q), on optimization variables a: = (x1, . . . .23\") and y = (y1, . . . ,ym), using the same A, b and c as above. max. 1 st. Am 5 b ATy 2 c b ' y c a: S 0 m, y 2 0 (a) Prove that if (P) is feasible and bounded, then (Q) is feasible and bounded. You will likely want to consider the optimal primal and dual assignments for (P) in your proof. (b) Prove that if a particular assignment of a: and y is feasible for (Q), the vector at is optimal for (P)