A Profit-maximization Model for a Company that Sells an Arbitrary Number of Products

Abstract

One of the problems faced by a firm that sells certain commodities is to determine the number of products that it must supply in order to maximize its profit. In this article, the authors give an answer to this problem of economic interest. The proposed problem is a generalization of the results obtained by Stirzaker (Probability and Random Variables: A Beginner's Guide, 1999) and Kupferman (Lecture Notes in Probability, 2009) where the authors do not present a situation where the sale of a quantity from some commodities is constrained by the marketing of another. In addition, the described procedure is simple and can be successfully applied to any number of commodities. The obtained results can be easily put into practice.