Chapter 6: Linear Programming Decisions

How can I improve my business?

Linear programming was originally developed by the American mathematician and Stanford University professor George Dantzig. It revolutionized the way in which organizations planned their operations. During the postwar period linear programming techniques were deployed to many industries, allowing them to make important decisions about product mix and production scheduling.¹ The original mathematical models used the linear simplex algorithm, which allowed optimal decision-making when constraints were present.

In business, the most common applications of linear programming include determining how to (1) maximize profits and revenues or (2) minimize costs. These decisions will be subject to constraints associated with resources, such as materials (input quantities), labor (time and manpower), capacity (production output), and demand (minimum or maximum sales). By determining an objective function—for example, to maximize the profits for a product line—and incorporating production constraints, an optimal solution can be found.