1. Sara Grossbaum and her sister Natalya inherited a manufacturing firm with the
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Question
1. Sara Grossbaum and her sister Natalya inherited a manufacturing firm with the same last name as a title. They manufacture or purchase component parts from a supplier in Milan, Michigan. The resulting profits (payoffs) of their end user consumer product is dependent upon the demand for the product. The following payoff table shows the projected profits ($000) of Nature State s1 (Low Demand) S2 (Medium Demand) S3 (High Demand) Action 45 85 Manufacture (D1) 175 20 Purchase (D2) 105 65 Prior Probability of .35 .35 State a. Produce the payoff table and find the expected payoffs. b. Produce the opportunity Loss (Regret) Table and find the expected opportunity losses of each action. b. Which action yields the best result and what is its expected opportunity loss? c. what is the EvPI? (expected value of perfect information) d. A test market study of the potential demand for the consumer product is expected to indicate unfavorable (U) results. The relevant conditional probabilities are as follows: P (u/s1) .40, P (u/s2) .40 and P (u/s3) s.20. ing Bayes rem, find the revised probabilities of the states. [Bayes' Thm.]Explanation / Answer
a)
Payoff table:-
States
Of
Nature
S1 (Low Demand)
S2 (Medium Demand)
S3 (High Demand)
Action
Manufacture (D1)
-45
85
175
Purchase (D2)
20
65
105
b)
Regret table:-
States
Of
Nature
S1 (Low Demand)
S2 (Medium Demand)
S3 (High Demand)
Action
Manufacture (D1)
65 (20-(-45))
0 (85-85)
0 (175-175)
Purchase (D2)
20 (20-20)
20 (85-65)
70 (175-105)
b)
payoff table with nature S3 and manufacture is preferred as it gives high results
c)
EVPI=EVwPI-EVwoPI (Maximum EMV)
States
Of
Nature
EMV
S1 (Low Demand)
S2 (Medium Demand)
S3 (High Demand)
Action
Manufacture (D1)
-45
85
175
-45(0.35)+85(0.35)+175(0.3)=66.5
Purchase (D2)
20
65
105
20(0.35)+65(0.35)+105(0.3)=61.25
EVwPI=20(0.35)+85(0.35)+175(0.3)=7+29.75+52.5=89.25
EVPI=89.25-66.5=22.75
States
Of
Nature
S1 (Low Demand)
S2 (Medium Demand)
S3 (High Demand)
Action
Manufacture (D1)
-45
85
175
Purchase (D2)
20
65
105
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