The Product-Mix (maximization) Problem

In a product-mix problem, there are two or more products (also called candidates or activities) such as TV models, competing for limited resources such as limited production capacity. The problem is to find out which products to include in the production plan and in what quantities these should be produced (product mix) in order to maximize profit, market share, or some other goal.

Although a solution to a product-mix problem does specify the quantities to be produced, what it tells more generally, in effect, is how to allocate scarce resources. This is because the technology of production given and once a decision has been made on the products and quantities to produce, the determination has actually been made of what resources to use and in what quantities.

Example:

The two models of color TV sets produced by the XYZ Corporation, will be designated as A and B. The company is in the market to make money; that is its objective is profit maximization. The profit realized is $300 from set A and $250 from set B. Obviously, more sets produced and sold, the better. The trouble is that there are certain limitations that prevent XYZ Corporation from producing and selling thousands of sets daily. These limitations are:

1. Availability of only 40 hours of labor each day in the production department (a labor constraint).
2. A daily availability of only 45 hours of machine time (a machining constraint).
3. Inability to sell more than 12 sets of model A each day (a marketing constraint).

XYZ Corporation problem is to determine how many sets of each model to produce each day so that the total profit will be as large as possible.

Answer Report