Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant, medium or large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars: Long-run Demand Plant Size Low Medium High Small 225 280 300 Medium 120 280 370 Large 75 280 750 Referring to Exhibit A, a. Identify the decision to be made, the decision alternatives, the chance event and the states of nature for this problem. b. What alternative should be chosen under the maximin criterion? Assume that the prior probabilities for low, medium and high demand are 0.2, 0.5 and 0.3, respectively. c. What is the recommendation if the Bayes' Decision Rule is used?
Exhibit A.
Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant, medium or large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:
|
|
Long-run Demand |
||
|
Plant Size |
Low |
Medium |
High |
|
Small |
225 |
280 |
300 |
|
Medium |
120 |
280 |
370 |
|
Large |
75 |
280 |
750 |
Referring to Exhibit A,
a. Identify the decision to be made, the decision alternatives, the chance event and the states of nature for this problem.
b. What alternative should be chosen under the maximin criterion?
Assume that the prior probabilities for low, medium and high demand are 0.2, 0.5 and 0.3, respectively.
c. What is the recommendation if the Bayes' Decision Rule is used?
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