The following payoff table shows profit for a decision analysis problem with two
ID: 453505 • Letter: T
Question
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:
State of Nature
Decision Alternative
S1
S2
S3
d1
300
150
75
d2
250
150
100
The probabilities for the states of nature are P(s1) = 0.45, P(s2) = 0.25, and P(s3) = 0.3.
(a)
What is the optimal decision strategy if perfect information were available?
S1
: - Select your answer -d1d2d1 or d2Item 1
S2
: - Select your answer -d1d2d1 or d2Item 2
S3
: - Select your answer -d1d2d1 or d2Item 3
(b)
What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place.
(c)
Using the expected value approach, what is the recommended decision without perfect information?
- Select your answer -d1d2Item 5
What is its expected value? If required, round your answer to one decimal place.
(d)
What is the expected value of perfect information? If required, round your answer to one decimal place.
State of Nature
Decision Alternative
S1
S2
S3
d1
300
150
75
d2
250
150
100
Explanation / Answer
State of Nature Decision Alternative S1 S2 S3 d1 300 150 75 d2 250 150 100 Probabilities 0.45 0.25 0.30 EMV of d1 = 300 * 0.45 + 150 * 0.25 + 75 * 0.30 = 135 + 37.5 + 22.5 = 195 EMV of d2 = 250 * 0.45 + 150 * 0.25 + 100 * 0.20 = 112.5 + 37.5 +30 = 180 Expected Value|Perfect Information It is calculated by multiplying highest payoff with respective probability. = 300 * 0.45 + 150 * 0.25 + 100 * 0.30 = 135 + 37.5 +30 = 202.50 Expected Value of Perfect Information Expected Value|Perfect Information - Highest EMV = 202.50 - 195 = 7.50 a. Optimal Decision Strategy State of Nature Decision Alternative S1 S2 S3 d1 300 150 75 d2 250 150 100 Decision d1 Indifferent d2 b. = 300 * 0.45 + 150 * 0.25 + 100 * 0.30 = 135 + 37.5 +30 = 202.50 c. Since d1 has highest EMV EMV of d1 = 300 * 0.45 + 150 * 0.25 + 75 * 0.30 = 135 + 37.5 + 22.5 = 195 d Expected Value of Perfect Information Expected Value|Perfect Information - Highest EMV = 202.50 - 195 = 7.50
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