Question

Problem 1.      Smoke Sensors, Inc. (SSI), is experiencing a tremendous growth in demand for its household smoke detectors. SSI produces both an AC model and a battery-operated model. It has an opportunity to be the exclusive supplier for a major department store chain, The Seers Company. Seers wishes to receive at least 20,000 AC models and 10,000 battery-operated models each week.

SSI's unanticipated prosperity has left it short of sufficient capacity to satisfy the Seer's contract over the short run. However, there is a subcontractor who can assist SSI by supplying the same types of smoke detectors. SSI must decide how many units it will make of each detector and how many units it will buy from the subcontractor. Data below summarize the production, price, and cost parameters.

Model

(hours per unit)

	AC	Battery	Hours available per week
Production Dept.	0.15	0.10	2,000
Assembly Dept.	0.20	0.20	4,200
Packaging Dept.	0.10	0.15	2,500
Total cost per unit	$20	$18

The subcontractor can supply any combination of battery or AC models up to 20,000 units total each week. The cost per unit to SSI is $21.50 and $20.00, respectively, for the AC and battery models. The contract with Seers calls for SSI to receive $25.00 for each AC model and $29.50 for each battery model.

Hint: Table below shows the possibilities.

	AC	Battery
SSI
Sub-Contract

1. Formulate the LP model which would allow SSI to determine the number of units of each type to produce and to buy to maximize total profit.
2. Use solver to solve the problem. Give the values of the decision variables, slacks, and the value of the objective function.

Answer 1