Applications of the "Unconscious Statistician" Theorem to profit maximization of a company that sells an arbitrary numbers of products

One of the problems faced by a firm that sells certain goods is to determine which is the number of products that must supply to maximize profits. In this article, we give an answer to this problem of economic interest. To solve it we use the theorem "unconscious statistician". The proposed problem is a generalization of the results obtained by Stirzaker and Kupferman where the authors do not present a situation where the sale of a quantity from some goods is constrained by the marketing of another. In addition, the described procedure is simple and can be successfully applied to any number of goods. The obtained results can be easily put into practice.