Consider the following primal-dual pair of linear programs Minimize Z = cx Maximize V = by (P) {Subject to Ax > 6 (D) Subject to Aty 0 y > 0 Let x and y be feasible solutions for (P) and (D) respectively. Show that a necessary and sufficient condition for both solutions to be optimal (for (P) and (D) respectively) is that we have n n (i) X; > 0) = d1jy + A2jY2 + ... + AmjYm = Cj Vj = 1, 2, (ii) 01jY1 + a2jY2 + ... + AmjYm 0 = 0;1X1 + di222 + ... + dinln = b; Vi = 1, 2, ..., m (iv) dilli + 0;222 + ... + dinilen > b; Yi = 0 Vi = 1, 2, ..., m