Prove Corollary 4.10 (complementary slackness) by first showing u∗b ≤ u∗Ax∗≤ cx∗.  Suppose that x and u are primal and dual feasible, respectively, and satisfy complementary slackness with respect to...

Prove Corollary 4.10 (complementary slackness) by first showing u∗b ≤

u∗Ax∗≤ cx∗.

 Suppose that x and u are primal and dual feasible, respectively, and

satisfy complementary slackness with respect to each other. Show that both

are optimal. Hint: Use complementary slackness for both the primal and the

dual; i.e., u(Ax − b)=(uA − c)x = 0.