Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For greater efficiency, Dwight always devotes the farm to growing one crop at a time. He now needs to make a decision on which one of four crops to grow during the upcoming growing season. For each of these crops, Dwight has obtained the following estimates of crop yields and net incomes per bushel under various weather conditions. Expected Yield, Bushels/Acre Weather Crop 1 Crop 2 Crop 3 Crop 4 Dry 20 15 30 40 Moderate 35 20 25 Damp 40 30 25 40 Net income per bushel $1.00 $1.50 $1.00 $0.50 Dry Moderate Damp 888 After referring to historical meteorological records, Dwight also estimated the following prior probabilities for the weather during the growing season: 0.3 0.5 0.2 40

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.  

B. Use Bayes’ decision rule to determine which crop to grow.  

C.Using Bayes’ decision rule, do sensitivity analysis with respect to the prior probabilities of moderate weather and damp weather (without changing the prior probability of dry weather) by re-solving when the prior probability of moderate weather is 0.2, 0.3, 0.4, and 0.6. . 

Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For greater efficiency,
Dwight always devotes the farm to growing one crop at a time. He now needs to make a decision on
which one of four crops to grow during the upcoming growing season. For each of these crops,
Dwight has obtained the following estimates of crop yields and net incomes per bushel under various
weather conditions.
Expected Yield, Bushels/Acre
Weather
Crop 1 Crop 2 Crop 3 Crop 4
Dry
20
15
30
40
Moderate
35
20
25
Damp
40
30
25
40
Net income per bushel $1.00 $1.50 $1.00 $0.50
Dry
Moderate
Damp
888
After referring to historical meteorological records, Dwight also estimated the following prior
probabilities for the weather during the growing season:
0.3
0.5
0.2
40
Transcribed Image Text:Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For greater efficiency, Dwight always devotes the farm to growing one crop at a time. He now needs to make a decision on which one of four crops to grow during the upcoming growing season. For each of these crops, Dwight has obtained the following estimates of crop yields and net incomes per bushel under various weather conditions. Expected Yield, Bushels/Acre Weather Crop 1 Crop 2 Crop 3 Crop 4 Dry 20 15 30 40 Moderate 35 20 25 Damp 40 30 25 40 Net income per bushel $1.00 $1.50 $1.00 $0.50 Dry Moderate Damp 888 After referring to historical meteorological records, Dwight also estimated the following prior probabilities for the weather during the growing season: 0.3 0.5 0.2 40
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