1) Cooke Collectibles produces fine porcelain miniatures representing famous people and historical events. To avoid production and scheduling problems, Cooke's policy is to make all copies of a figure in one production run. In the event that the demand for any figure exceeds the number produced, each customer's money is returned along with a coupon good for $11.00 toward the purchase of another Cooke miniature. If the company makes too many figures, the extras are sold to a discount outlet, which agrees to hold them for six months, for $53.00 each. This price is half the variable production cost of a figure. Cooke Collectibles has recently agreed to pay $199000 for the rights to produce a miniature representing a famous singer. The company plans to sell the figures for $247 each. The marketing department predicts that actual demand will equal one of these possible demand levels: 20,000; 40,000; 60,000; or 80,000. Suppose the marketing manager at Cooke Collectibles has analyzed the possible demand levels and subjectively assessed the following probabilities for them.
20,000 0.1
40,000 0.34
60,000 0.28
80,000 0.28
Find the associated expected value for each level.
EV(20,000) = $
EV(40,000) = $
EV(60,000) = $
EV(80,000) = $
2) The production manager for a video-game company has been asked to help upper management decide whether to market a new game based on a popular cartoon character. If the new game is successful, the company will make $45 million; but, if it is a failure the company will lose an estimated $25 million in production and advertising expenses. Suppose that marketing personnel have determined there are several levels of success and failure possible with the proposed video game. The possibilities (states of nature) and the assessed probabilities are as follows.
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Success Level
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Probability
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Excellent ($71000000)
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0.29
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Good ($45000000)
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0.28
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Fair ($6000000)
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0.13
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Poor ($-25000000)
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0.3
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Find the Expected Value of Marketing.
3) Far Horizons Development Corporation, which is considering building a vacation condominium project on the Maine coast, is trying to decide how many units to build. Because of their central-utility design, the units must be built in blocks of 10. Assume that, for each block of 10, the land will cost $183000 and construction will cost $232000 plus an additional $59000 for each unit. Given that the company has decided to build, the possible production levels are as follows: 10, 20, 30, 40, 50. Each unit will be priced at $215000 for the regular market. However, if demand does not meet supply, Far Horizons will be forced to auction the units at an average price of $75000. Set up a payoff table assuming the following possible demand levels: 0, 10, 20, 30, 40, 50.
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Demand
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Build
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0
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10
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20
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30
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40
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50
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10
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?
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20
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30
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40
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50
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