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
A.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 expected value of the
C.What is the efficiency of the information?
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