Problem3 Old MacDonald is the manager of a large farm with 5,000 acres of arable

Question

Problem3 Old MacDonald is the manager of a large farm with 5,000 acres of arable land. For greater efficiency, he always grows just one crop on the farm at a time. It is now time to decide what crop from the four choices will be grown during the upcoming growing season. For each of these crops, MacDonald has obtained the following estimates of crop yields and net incomes per bushel under various weather conditions. Expected Yield, Bushels per acre Weather Dry Moderate Damp Net Income per bushel Crop 1 20 35 40 Crop 2 15 20 30 Crop 3 30 25 25 Crop 4 40 4040 $1.00 $1.50 $1.00 S0.50 After referring to historical meteorological records, MacDonald also estimates the following prior probabilities for the weather during the growing season. Weather Prior Probability 0.25 0.55 0.20 Dry Damp a. What decision should be made according to the maximax b. What decision should be made according to the maximin c. What decision should be made according to the minimax d. What decision should be made according to the expected e. Based on the analysis in parts a-d, what would you decision rule? decision rule? regret decision rule value decision rule? ultimately recommend?

Explanation / Answer

a. according to the maximax decision rule

b. . according to the maximin decision rule

c. . according to the minimax decision rule

d. Expected value decision rule

maximax decision Dry Moderate Damp Net income max Crop1 20 35 40 $1 40 maximax Crop2 15 20 30 $1.50 30 Crop3 30 25 25 $1 30 crop4 40 40 40 $0.50 40

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