A profit-maximization model for a company that sells an arbitrary number of products

One of the problems faced by a firm that sells certain commodities is to determine the number of products that it must supply with in order to maximize profits. In this article, the authors give an answer to this problem of economic interest. To solve it they use the theorem of the "unconscious statistician". 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.