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Consider a manufacturer of perfume who is about to expand production capacity to make a new product. Three alternative production processes are available. The following table shows the estimated profits (in $) for these processes for each of the three possible demand levels for the product. Alternatives States of Nature Low demand Moderate demand High demand A 100,000 350,000 900,000 B 150,000 400,000 700,000 C 250,000 400,000 600,000 Suppose that the manufacturer assigns prior probabilities of 0.20 to low demand, 0.30 to moderate demand and 0.50 to high demand. Based on the above information, what is the amount of expected payoff under certainty?

Question

Consider a manufacturer of perfume who is about to expand production capacity to make a new product. Three alternative production processes are available. The following table shows the estimated profits (in $) for these processes for each of the three possible demand levels for the product. Alternatives States of Nature Low demand Moderate demand High demand A 100,000 350,000 900,000 B 150,000 400,000 700,000 C 250,000 400,000 600,000 Suppose that the manufacturer assigns prior probabilities of 0.20 to low demand, 0.30 to moderate demand and 0.50 to high demand.

Based on the above information, what is the amount of expected payoff under certainty?

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Solution

The expected payoff under certainty is not applicable in this scenario. The concept of "payoff under certainty" refers to the situation where the outcome is certain, i.e., we know for sure which state of nature (demand level in this case) will occur. However, in this case, the manufacturer is uncertain about the demand level - it could be low, moderate, or high. Therefore, we cannot calculate the payoff under certainty.

What we can calculate is the expected monetary value (EMV) for each alternative, which is a weighted average of the payoffs under each state of nature, with the weights being the probabilities of the states of nature. The EMV gives us the average payoff we would get if we could repeat the decision situation many times.

Here's how to calculate the EMV for each alternative:

EMV(A) = 0.20100,000 + 0.30350,000 + 0.50900,000 EMV(B) = 0.20150,000 + 0.30400,000 + 0.50700,000 EMV(C) = 0.20250,000 + 0.30400,000 + 0.50*600,000

The alternative with the highest EMV is the best decision according to the expected monetary value criterion.

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