For the next two parts, let A be a matrix in Rm n with linearly independent rows, let b be a vector in Rm and c be a vector in Rn. Let us be given a primal-dual pair of LPs max{cTx : Ax = b, x 0} . and min{bTy : ATy c} (P) (D) Recall that strong duality implies that if (P) or (D) has an optimal solution then both (P) and (D) have optimal solutions and the optimal values of these LPs are equal. In this question we will further consolidate the relationships you have been learning between duality, complementary slackness and geometry. (a) Let x and y be optimal solutions for (P) and (D), respectively. Let (AT)=y = c= denote the tight constraints for y in ATy c. Prove that if (AT)= has m rows and rank((AT)=) = m, then x is a basic feasible solution of (P)