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Problem1.     Smoke Sensors, Inc. (SSI), is experiencing a tremendous growth indemand for its household smoke detectors. SSI produces both an ACmodel and a battery-operated model. It has an opportunity to be theexclusive supplier for a major department store chain, The SeersCompany. Seers wishes to receive at least 20,000 AC models and10,000 battery-operated models each week.

SSI's unanticipated prosperity hasleft it short of sufficient capacity to satisfy the Seer's contractover the short run. However, there is a subcontractor who canassist SSI by supplying the same types of smoke detectors. SSI mustdecide how many units it will make of each detector and how manyunits it will buy from the subcontractor. Data below summarize theproduction, price, and cost parameters.

Model

(hours perunit)

	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 anycombination of battery or AC models up to 20,000 units total eachweek. The cost per unit to SSI is $21.50 and $20.00, respectively,for the AC and battery models. The contract with Seers calls forSSI to receive $25.00 for each AC model and $29.50 for each batterymodel.

Hint: Table below shows thepossibilities.

	AC	Battery
SSI
Sub-Contract

1. Formulate the LP model which would allow SSI to determine thenumber of units of each type to produce and to buy to maximizetotal profit.
2. Use solver to solve the problem. Give the values ofthe decision variables, slacks, and the value of the objectivefunction.