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).The state-of-nature probabilities are P(s1) = .35, P(s2) = .35, and P(s3) =30.a. Use a decision tree to recommend a decision.b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.c. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditionalprobabilities are as follows: P(F | s1)= .10 P(U | s1) = .90 P(F | s2) = .40 P(U | s2) = .60 P(F | s3) = .60 P(U | s3) = .40 What is the probability that the market research report will be favorable?d. What is Gorman’s optimal decision strategy?e. What is the expected value of the market research information?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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).
The state-of-nature probabilities are P(s1) = .35, P(s2) = .35, and P(s3) =30.
a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.
c. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional
probabilities are as follows:
| P(F | s1)= .10 | P(U | s1) = .90 |
| P(F | s2) = .40 | P(U | s2) = .60 |
| P(F | s3) = .60 | P(U | s3) = .40 |
What is the probability that the market research report will be favorable?
d. What is Gorman’s optimal decision strategy?
e. What is the expected value of the market research information?
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