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

TL;DR

This paper presents a profit-maximization model for companies selling multiple products, extending previous models by considering constraints between product sales, with a simple procedure applicable to any number of commodities.

Contribution

It generalizes existing profit-maximization models to include multiple products with interdependent sales constraints, providing a practical and straightforward solution.

Findings

Model accommodates any number of products

Procedure is simple and easy to implement

Results are directly applicable in real-world scenarios

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.