Hartman Electronics is a small retail electronics store. Among the items they sell are two different DVD players from a particular manufacturer. There is a base model and a deluxe model. They are planning inventory orders for the next three months; they place orders with the manufacturer on the first of each month. The anticipated demand over the next three months is represented in the following table:
Month Model Model
April 400 300
May 700 400
June 375 325
The manufacturer can provide Hartman with up to 500 Base model DVD’s each month at a price of $65 apiece. Anything beyond 500 will require a different production process, so the cost will go up to $70 apiece. The manufacturer can provide Hartman with up to 300 Deluxe model DVD’s each month at $90 apiece. Anything above 300 will cost $96 apiece, for the reasons stated above. Hartman can order more than enough units to cover anticipated demand in one month, and hold the excess units in inventory to help satisfy demand in a subsequent month. Hartman estimates an inventory holding cost of $2.00 per unit, of either model, from one month to the next. Hartman is limited to holding no more than 100 total DVD’s from one month to the next.
Formulate a linear program that will help Hartman to determine the order schedule that will allow him to minimize the cost of obtaining enough DVD’s to satisfy demand. The linear program should include complete descriptions of the decision variables, a statement of the objective function, and all relevant constraints.