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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. Weather Dry Moderate Damp Net income per bushel Dry Moderate Damp Expected Yield, Bushels/Acre 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 Crop 1 Crop 2 Crop 3 Crop 4 20 15 30 40 35 20 25 40 40 30 25 40 $1.00 $1.50 $1.00 $0.50

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. Weather Dry Moderate Damp Net income per bushel Dry Moderate Damp Expected Yield, Bushels/Acre 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 Crop 1 Crop 2 Crop 3 Crop 4 20 15 30 40 35 20 25 40 40 30 25 40 $1.00 $1.50 $1.00 $0.50

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.FOM: Focus On Modeling: Making The Best Decisions
Problem 7P: Cell Phone Plans Gwendolyn is mulling over the three cell phone plans shown in the table. Gigabytes...
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 Use Bayes’ decision rule to determine which crop to grow. 

 

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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