## An elementary proof of linear programming optimality conditions without using Farkas’ lemma

Although it is easy to prove the sufficient conditions for optimality of a linear program, the necessary conditions pose a pedagogical challenge. A widespread practice in deriving the necessary conditions is to invoke Farkas’ lemma, but proofs of Farkas’ lemma typically involve “nonlinear” topics such as separating hyperplanes between disjoint convex sets, or else more … Read more