combinatorial optimization. One aspect of linear programming which is often forgotten is the fact that it is al o a useful proof technique. In this rst chapter, we describe some linear …

Use the simplex algorithm. Use artificial variables. Describe computer solutions of linear programs. Use linear programming models for decision making.

As we study linear programming, we’ll quantify these terms in a mathematically precise way. For the time being, let’s agree that when we optimize something we are trying to make some …

Most linear programming (LP) problems can be interpreted as a resource allocation problem. In that, we are interested in defining an optimal allocation of resources (i.e., a plan) that …

To illustrate some of the basic features of LP, we begin with a simple two-dimensional example. In modeling this example, we will review the four basic steps in the development of an LP model: …

The first chapter introduces key concepts in linear programming and contributes a new cognitive framework to help students and practitioners set up each optimization problem.

Graphical solution approaches to solve two-variable linear models are used to illustrate how linear programming algorithms solve models containing many more variables as are typical of most …