Spaces, Cones, Bases and Extreme Points

Abstract

In previous chapters we learned how to set up LP problems, their economic interpretation and the proper relations between their primal and dual specifications. In this chapter we will examine more closely the geometric and algebraic structure of a linear programming model. For ease of exposition and graphing, we will discuss a very simplified linear programming problem with only two outputs and two inputs because we want to graph it in two-dimensional diagrams. Every notion and result presented here, however, can be extended to more complex LP formulations with many hundreds and even thousands of outputs and inputs.