This is a mathematical technique to obtain a solution for a maximization (or minimization) problem. The goal is to maximize a function called the objective function, subject to constraints.
Both the objective function and the constraints, are linear functions.
1. A product-mix problem. Maximize profits, for instance, a profit function as a function of the production level of, say, two products subject to time constraints to manufacture both products.
2. Allocation of advertising budget. Maximize a function that represents the number of "audience points" from three media (radio, TV, and newspapers), subject to constraints representing, for instance, the total budget and the cost of each media, minimum amounts spent on each media, and non-negativity constraints.
Render, B. and R.M. Stair, Jr. (1997): Quantitative Analysis for Management. Sixth Edition. Prentice Hall.
Turban, E. and J.R. Meredith (1985): Fundamentals of Management Science. Third Edition Business Publications, Inc.