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.

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: …

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 …

How to recognize a solution being optimal? How to measure algorithm effciency? Insight more than just the solution? What do you learn? Necessary and Sufficient Conditions that must be …

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 …

Linear programming is an important branch of applied mathematics that solves a wide variety of optimization problems. It is widely used in production planning and scheduling problems.