Defining the Problem The problem to be solved is to determine various factors involved in the selling of their tablet computer: GMTab365. As a final goal we will be determining the selling price and production level to maximize average profit per item, and that fits within reasonable production levels and the overall goals of GMC. GMC believes that the maximum price they could sell a tablet computer is $2000. However, for each additional 100 computers they want to sell, the price must be reduced by $6 (or put another way, for each computer sold, the price must be reduced by $0.06). Furthermore, there is a fixed cost of $100,000 with a marginal cost of $250 per computer.

Making Assumptions

GMC has many choices as to what to produce and sell. They are seeking a production level that maximizes the return on their investment. The Human Resource Department has raised the question of whether maximizing profit per unit might lead to a low production level and cause layoffs, and management is committed to avoiding large layoffs. The Finance Department points out that the goal will not be to maximize profit per unit. Also, flexibility exists to allocate resources elsewhere for the production of other computer-related items, and those employees can be placed on other projects. Therefore, the goal will be to maximize profits (not profit per unit). Management is looking to you for recommendation on what function should be maximized, subject to what constraints.

Defining Variables

The variables in the problem are:

x = the level of production of computers

p = the price to sell the computers based upon projected demand levels

R = the revenue gained based on production level

C = the cost based on production level

P = the profit based on production level

AP = the average profit per computer at based on production level