Profit Maximization In A Product Mix Company Using Linear Programming

Abstract

This paper demonstrates the use of linear programming methods as applicable in the manufacturing industry. Data were collected as extracts from the records of KASMO Industry Limited, Osogbo, Nigeria, on four types of sales packages adopted for selling her medicated soap product which include 1 tablet per pack, 3 tablets per pack, 12 tablets per pack and 120 tablets per pack. Information on selling price per pack and on the cost of five basic raw materials used as well as the quantity of each of the raw material held in stock per month for the production of soap tablets were available in the records of the company. Based on the costs of raw materials, the maximum profit that would accrue to the company given the product mix was determined. The results showed that the company would attain optimal monthly profit level of about N271,296 if she concentrates mainly on the unit sales (one tablet per pack) of her medicated soap product, ignoring other forms of sales packages. By this, her sales turn-over per month would be about 18,900 soap tablets. The analysis was carried out with R statistical package (www.cran.org) using the library “lpSolve”.

Key Words: Linear programming, Simplex Method, Objective function, Product mix, R software.