Carry out a preposterior analysis and, using the revised probabilities, determine (1) the expected monetary value when the weather conditions are favorable and (2) the expected monetary value when the weather conditions are poor.
Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars.
The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. Based on this information, the prior probabilities have been revised. If the weather conditions are favorable, P(S1) = .4286, P(S2) = .5357, and P(S3) = .0357; and if the weather conditions are poor, P(S1) = .1364, P(S2) = .6818, and P(S3) = .1818. It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44
Choose strategy 1; EMV1 = 92.50. (2) Choose strategy 2; EMV2 = 99.09.
If weather conditions are favorable, then the following expected monetary value calculations are performed.
EMV1 = (.4286)(110) + (.5357)(80) + (.0357)(70) = 92.50
EMV2 = (.4286)(60) + (.5357)(120) + (..0357)(50) = 91.79.
Since 92.5 > 91.79, choose strategy 1.
If the weather conditions are poor, then the following expected monetary value calculations are performed:
EMV1 = (.1364)(110) + (.6818)(80) + (.1818)(70) = 82.28
EMV2 = (.1364)(60) + (.6818)(120) + (.1818)(50) = 99.09.
Since 99.09 > 82.28, choose strategy 2.
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