State of Nature High (0.2) Moderate (0.5) Low (0.3) $80,000 60,000 70,000 $60,00

Question

State of Nature High (0.2) Moderate (0.5) Low (0.3) $80,000 60,000 70,000 $60,000 40,000 50,000 (-$10,000) 30,000 20,000 Small facility Alternative Medium faity Large facility 03. The choice for the MINIMAX criterion would be (2pts): a. Small b. Mediumc. Large b. Mediunm b. Mediumc. Large d. High d. High d. High e. $80,000 -04. The choice for the MAXIM IN criterion would be: a. Small c. Large e. Low -05. If P (High-02; Moderate-05; Low:03), the choice for the maximum expected value (EMV) criterion would be: a. Small e. Moderate 06. The value of EPPI (or EVwPI) would be: a. $29,000 b. $37,000 c. $50,000 d. $55,000 e. None of the above 07. The value of EVPI would be: a. $ 13,000 b. $10,000 c. $14,000 d. $12,000 e. None of the above

Explanation / Answer

Ans 6)

To find the Expected profit with perfect information(EPPI), we first need to find the optimal course of action(highest profit) for each state of nature.

For 'High' state of nature, optimal course of action = $80,000 (Small facility)

For 'Moderate' state of nature, optimal course of action = $60,000 (Small facility)

For 'Low' state of nature, optimal course of action = $30,000 (Medium facility)

The Expected profit with perfect information is the summation of the product of the probability of occurrence of a state of nature and the optimal course of action for that state of nature.

Expected profit with perfect information(EPPI) = 0.2 * 80000 + 0.5 * 60000 + 0.3 * 30000

= $55,000

Hence the correct answer is option D.

Ans 7)

The expected value of perfect information (EVPI) = EPPI - EMV

where EPPI = Expected profit with perfect information and EMV = Expected monetary value

The Expected Monetary Value (EMV) is the highest expected payoff out of all the possible courses of action.

The expected payoff for 'Small facility' course of action = 0.2 * 80000 + 0.5 * 60000 + 0.3 * (-10000)

= $43,000

The expected payoff for 'Medium facility' course of action = 0.2 * 60000 + 0.5 * 40000 + 0.3 * 30000

= $41,000

The expected payoff for 'Large facility' course of action = 0.2 * 70000 + 0.5 * 50000 + 0.3 * 20000

= $45,000

The highest expected payoff is for the 'Large facility' course of action. Hence the Expected Monetary value is $45,000.

Now.

Expected value of perfect information (EVPI) = EPPI - EMV

= $55,000 - $45,000

= $10,000

Hence the correct answer is option B.

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