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# LINEAR PROGRAMMING WITH PYTHON AND PULP

Journal: International Journal of Industrial Engineering Research and Development (Vol.9, No. 3)

Publication Date:

Authors : ;

Page : 1-8

Keywords : Constraints; Feasible region; GLPK solver; Objective function; Optimization; and PuLP.;

### Abstract

Linear Programming is a family of mathematical programming that is concerned with the allocation of scarce or limited resources i.e. raw materials, partially finished products, labour, investment capital or time to several competing activities on the basis of given optimality. It is employed in operation research for the purpose of optimization of linear functions subject to linear equality and inequality constraint. An optimal allocation may be one that maximizes some measure of benefit or utility, such as profit, or minimizes some measure of cost. The technique of linear programming is used in wide range of applications, including agriculture, industry, transportation, economic, health system, social science, and military. In this paper we will solve a linear programming problem using python language. As an analyst, we try to find a good optimal solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem. The objective of this paper is to find the best mix that maximizes profit. To obtain the solution to this Linear program, we have to write a short program in Python to call PuLP's modeling functions, which will then call a solver. Then we will obtain the graph using python commands, which will give the shaded area enclosed by the constraints called feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profits 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.