complementary slackness

A feasible primal x and feasible dual y are both optimal if and only if, for every constraint pair, either the constraint holds with equality or its paired variable is 0 (or both). The LP-specific instance here (complementary-slackness-lp) is the same idea Chapter 6's general KKT system already established for a constrained optimum broadly (kkt-complementary-slackness), specialized to a linear objective and linear constraints -- and it runs in both directions, letting either optimal solution be recovered from the other with no second LP solved.