Chapter 4, Operations Research (or)

In the last chapter, we introduced the concept of a basis of a linear program (P) Minimize Z = c T x s.t. Recall that a basis of (P) is a subset B ⊆ {1, 2,. .. , n} of the variables. We also introduced the concepts of a basic solution x B of (P), and a dual basic solution y B associated with B and the dual (D) of (P). We finished by proving Lemma 1 Let B be an arbitrary basis for (P). If B is a feasible basis for both (P) and (D), then x B is optimal for (P), and y B is optimal for (D).