
2
Geometry of Linear Programming
2.1 Introduction
In this chapter, we explore the geometry of linear programming and gain
geometric insight into optimal solutions. Also, the corresponding algebraic
representations of the geometry are developed. This leads to the Fundamental
Theorem of Linear Programming, which serves as the basis for algorithm
development for linear programs.
2.2 Geometry of the Feasible Set
We have seen that the feasible set for a linear program can be bounded, un-
bounded, or infeasible. In this section, we explore additional geometric prop-
erties of feasible sets of general linear programs that are consistent, i.e., whose
feasible