LINEAR PROGRAMMING IN MATLAB

Abstract

Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimise their use of planes and staff. NASA has been using them for many years to optimize their use of limited resources. Oil companies use them to optimise their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In this paper, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for its optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the productmix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this paper is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit which still touches the feasible region