Linear programming problems involve the optimization of a linear function, called the objective function, subject to linear constraints, which may be either equalities or inequalities. Although the origin of linear programming as a mathematical discipline is quite recent, linear programming is now well established as an important branch of applied mathematics due to its wide applicability.

In order to understand the theory of linear programming and the methods used to solve linear programming problems, it is essential to have a geometric understanding of these problems. In this talk, I will introduce the relevant geometrical concepts associated with a linear program and their algebraic characterizations. If time permits, I will discuss the Simplex Algorithm, a generalized algorithm for linear programming that exploits the special geometry of a linear program.

No prior knowledge of linear programming is assumed for this talk. However, one should be comfortable with basic linear algebra.