Linear Programming Problem: Applications and Generalizations of Linear Programming

Abstract

This paper describes LinearProgramming, an important generalization of Linear Algebra. Linear Programmingis used to successfully model numerous real world situations. In many of theseproblems, the number of variables and constraints are so large that it is notenough too merely to know there is solution; we need some way of finding it (orat least a close approximation to it) in a reasonable amount of time. Wedescribe the types of problems Linear Programming can handle and show how wecan solve them using the simple method. We discuss generalizations to BinaryInteger Linear Programming (with an example of a manager of an activity hall),and conclude with an analysis of versatility of Linear Programming and thetypes of problems and constraints which can be handled linearly, as well assome brief comments about its generalizations.