ABSTRACT
Mathematical programming is the area of mathematics that is concerned with optimizing an objective function of several variables subject to constraints on those variables. The problems studied in this chapter are more tractable, though they are still non-trivial and have wide applications. The underlying idea of the problem is to optimally allocate limited resources. The objective function will be linear, the constraints will be linear, and the variables will usually take values in subsets of the non-negative half of the real line. The chapter considers the graphical solution of LP problems in two variables. It uses the geometric intuition to derive some of the general theory that leads to an approach to higher dimensional problems. The chapter describes the so-called simplex algorithm to solve the standard maximum problem and uses the important notion of duality between problems to extend the approach to standard minimum problems.
