Linear programming is a relatively new, very important branch of modern mathematics and is about twenty five years old. In this day and age, most planners and decision makers will acknowledge that some linear optimization problems are worth the expense and trouble to solve. Using linear programming technique as a tool to make decision plannes are able to greatly redice cost or increase profit for any project under consideration. Since Dr. George B. Dantzig published his first paper on the simplex method in 1947, progress in that field has been rapid. Although the first applications were military in nature, it was not long before it became apparent that there were important economic and industrial applications as well. Typical areas of application in linear programming are inventory control, quality control, production scheduling, forecasting, maintenance and repairs, process design, accounting procedures, capital budgeting, the diet problem, machine- loading problem, and the transportation problem.