Maximizing Profit at Computer Flips

Today we learned about maximizing profits, using a Junior Achievement Company called Computer Flips as an example.

Computer Flips sells two computer models, the Simplex and the Omniplex. The Simplex has fewer add-ons and can be completed in a shorter time, and the Omniplex has more add-ons and takes twice as long to complete. Students at the company only work a certain amount of time each week, which factors in to how many models can be made.

The production manager of the company must decide the rate of production per week of each computer model in order to maximize the company's weekly profit. The point at which the profit is maximized is called the optimal solution.

In order to make this kind of decision, we use a technique called linear programming.

First we began by making guesses on how many models the company should produce and testing what the profits would be. Although certain combinations resulted in high profits, we found that there wouldn't be enough installation time to actually make that number of each model.

After we found which amounts of the models could be made to maximize profits and also be completed in the given installation time, we needed to write an equation of the amount of weekly profit, z. z is a function of x1 (the weekly production rate for Simplex) and x2 (the weekly production rate for Omniplex). This is called an objective function because the objective is to maximize profit, and the variables are called decision variables because they will help the production manager make his decision.

The equation was written as an inequality that showed the relationship between the installation time required to produce x1 and x2 each week, and the amount of available installation time each week.

To graph the equation, we replaced x1 and then x2 with 0 in order to find the intercepts. Once we had these points, we were able to draw a line on the graph.

The line of the equation creates an area on the graph called the feasible region, which contains all points that represent feasible, or possible, production mixes. They are constrained into this area because there is only a certain amount of installation time each week.

Combinations of the two computer models that will result in the largest profits will be in the feasible region.