Linear programming was developed by applied mathematicians and operations research specialists as a means to solve real-world problems using linear methods. Based on the fundamentals of matrix algebra, linear programming seeks to find an optimal solution, using quantitative methods, to a particular problem given a finite number of constraints. It is used extensively in managerial science and has widespread utility to business, government, and industry. It is applied especially to problems in which decision-makers wish to minimize costs or maximize profits under a given operating construct. In many cases, linear programming will affect decisions regarding materials used in manufacturing and construction or even the hiring of personnel or particular skill sets. It is an excellent tool for decisions regarding resource allocation.

Linear programming is based on linear equations—equations of variables raised only to the first power. Many variables--such as x, y, and z) or...