(P)Minz=cxAx=bx0 (D) {Maxw=ubuAc Let us denote by Aj the j th column of A. Prove that two solutions (x,u) of, respectively, (P) and D) are optimal if and only if (uAjcj)xj=0,j=1,,n (P)Minz=cxAx=bx0 (D) {Maxw=ubuAc Let us denote by Aj the j th column of A. Prove that two solutions (x,u) of, respectively, (P) and D) are optimal if and only if (uAjcj)xj=0,j=1,,n