Part I: Clay Whybark, a soft-drink vendor at Hard Rock Cafe's annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd):
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States of Nature (demand)
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Alternatives
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Big
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Average
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Small
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Large stock
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S22.000
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S 12.0(x)
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-52.000
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Average stock
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SI 4,000
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S 10.000
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S6.000
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Small stock
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S 9.000
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S 8.000
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54.000
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The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand.
a) Determine the alternative that provides Clay Whybark the greatest expected monetary value (EMV).
b) Compute the expected value of perfect information (EVPI).
Part II: The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Amber Gardner's software firm:
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Demand
Low High
Alternative 1 $10,000 $30,000
Alternative 2 $ 5,000 $40,000
Alternative 3 -s 2.0(X) $50,000
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The probability of low demand is 0.4, whereas the probability of high demand is 0.6.
a) What is the highest possible expected monetary value?
b) What is the expected value with perfect information (EVwPI)?
c) Calculate the expected value of perfect information for this situation.
Part III: The University of Dallas bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 90 operations management students enrolled, but bookstore manager Curtis Ketterman has second thoughts, based on his intuition and some historical evidence. Curtis believes that the distribution of sales may range from 70 to 90 units, according to the following probability model:
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Demand
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70
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75
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80
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85
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90
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Probability
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.15
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.30
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.30
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.20
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.05
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This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $36.
a) Construct the table of conditional profits.
b) How many copies should the bookstore stock to achieve highest expected value?