# Charles River Jazz Festival

Topics: Decision theory, Arithmetic mean, Money Pages: 2 (500 words) Published: November 11, 2012
1. Decision tree for Friday pressing
Mr. Ward is trying to decide on how many CDs to press on the first night of the festival. His intuition combined with his experience allowed him to make some predictions of demand. These take the form of probabilities. “The probabilities may be subjective estimates from managers or from experts in a particular field, or they may reflect historical frequencies. If they are reasonably correct, they provide a decision maker with additional information that can dramatically improve the decision-making process.” Since the problem is limited to Ward’s expected demands for CDs, we can say that our recognizable states of nature are the following: Saturday Demand = 1000 and Sunday Demand = 1000

Saturday Demand = 1000 and Sunday Demand = 3000
Saturday Demand = 3000 and Sunday Demand = 1000
Saturday Demand = 3000 and Sunday Demand = 3000
The minimum total demand for both Saturday and Sunday would be 2000 CDs, whereas the maximum total demand for both Saturday and Sunday would be 6000 CDs. The intermediate total demand however is consistent at 4000 CDs. We can consolidate them to 3 states of nature: Saturday Demand + Sunday Demand = 2000

Saturday Demand + Sunday Demand = 4000
Saturday Demand + Sunday Demand = 6000
Let’s call these states of nature d2, d4 and d6.
We use the TreePlan software to create the decision tree for Ward’s problem. We specified the initial costs of productions as \$24,000, \$33,000 and \$42,000. Additionally, we make sure to deduct the royalties from the sales revenue, since they are considered as future expenses (after the sales occur). Please see below for the decision tree.

2. Maximization of Expected Monetary Value as a criterion
The average or expected payoff of each alternative is a weighted average: the state of nature probabilities are used to weight the respective payoffs. ¹ Therefore the expected monetary value for each alternative is as follows: EMVp2 = \$ 6,000

EMVp4 = \$ 12,000...

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