MA87 Problem: Decision Analysis under Uncertainty – Slick Ltd

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MA87 Problem: Decision Analysis under Uncertainty – Slick Ltd.

 

Slick Ltd. produces a product called Zap. The president of Slick Ltd. is currently attempting todecide on an appropriate selling price for each unit of Zap for the upcoming year. He realizedthat a higher price would naturally result in lower demand, but he also felt that the actual finaldemand would depend on whether the state of the economy next year is weak or strong.His situation is further complicated because he must purchase his entire materials requirementfor next year’s production of Zaps in a single lot of either 200,000 units or 240,000 units, and theunit price of these materials will depend on the size of the lot he orders, 200,000 or 240,000. Thesole supplier of the materials will accept no additional orders during the year. Therefore, if Slick Ltd. does not purchase enough materials to meet actual demand, some orders will be left unfilled.On the other hand, if more materials are purchased than are required to fill demand, the excessmaterials will become spoiled at the end of the year and Slick Ltd. will have to scrap the spoiledmaterials.The president has summarized the cost of materials data and his expected overall demandsituation for the next year as follows:

Quantity of Materials OrderedCost per Unit

200,000 units $3.00240,000 units 2.90 Note: each unit of Zap requires one unit of materials.Expected Demand for Zap:

State of EconomyUnit Selling Price Weak (p = .6)Strong (p = .4)

$5.25 180,000 200,000$5.00 200,000 240,000

Required

Determine the quantity of materials that should be ordered for next year’s production of Zap, andthe selling price for one unit of Zap that will provide Slick Ltd. with the highest expectedcontribution next year. Assume that all other costs in the production of Zap remain constantregardless of the quantity produced. Show all supporting calculation

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