Peter Shor teaches lecture 13 of MIT's 18.200 Principles of Discrete Applied Mathematics, extending linear programming duality beyond canonical form. He shows how to construct dual programs for arbitrary primal linear programs, introduces complementary slackness conditions linking primal and dual optimal solutions, and presents a physics-inspired proof of strong duality, framing the LP as a system in equilibrium. The lecture closes by applying strong duality to prove Koenig's theorem, connecting the abstract optimization machinery to a concrete result in graph theory about matchings and vertex covers in bipartite graphs. The 76-minute session is blackboard-based, with Shor working through proofs and arguments step by step for students who have already covered basic LP formulation and canonical duality earlier in the course.