The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 Compute the probabilities by completing the table Sate of nature prior probabilities P(S1) Consultant's Record P(F|S1) Joint probabilities P(F and S1) Conditional probabilities P(s1|F) s1 s2 s3 Sate of nature prior probabilities P(S1) Consultant's Record P(U|S1) Joint probabilities P(U and S1) Conditional probabilities P(s1|U) s1 s2 s3 B. What is the probability that the market research report will be favourable? C. What is the probability that the market research report will be unfavorable?
The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):
state of nature
| low demand | medium demnad | high demand | |
| Decision alternative | s1 | s2 | s3 |
| manufacture d1 | -20 | 40 | 100 |
| purchase d2 | 10 | 45 | 70 |
The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30.
a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows:
P(F|S1)=0.10 P (U|S1)=0.90
P(F|S2)=0.40 P (U|S2)=0.60
P(F|S3)=0.60 P (U|S3)=0.40
Compute the probabilities by completing the table
| Sate of nature |
prior probabilities P(S1) |
Consultant's Record P(F|S1) |
Joint probabilities P(F and S1) |
Conditional probabilities P(s1|F) |
| s1 | ||||
| s2 | ||||
| s3 |
| Sate of nature |
prior probabilities P(S1) |
Consultant's Record P(U|S1) |
Joint probabilities P(U and S1) |
Conditional probabilities P(s1|U) |
| s1 | ||||
| s2 | ||||
| s3 |
B. What is the probability that the
C. What is the probability that the market research report will be unfavorable?
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