 Business
16 December, 02:03

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 upcominggrowing 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 Crop 1 Crop 2 Crop 3 Crop 4Dry 20 15 30 40Moderate 35 20 25 40Damp 40 30 25 40Net income/bushel \$1.00 \$1.50 \$1.00 \$0.50After referring to historical meteorological records, Dwight also estimated the following probabilities for the weather during the growing season:Dry 0.3Moderate 0.5Damp 0.2Required:1. Construct a decision tree and use Bayes deicison fule to determine which crop to grow?

+2
1. 16 December, 03:14
0
crop 1

Explanation:

The tree will consist of two branches the probabilities branch and the decision branch

The probability will calculate the probability of each crop in all weather conditions as follows

crop 1 = (20*0.3) + (35*0.5) + (40*0.2) = 31.5

crop 2 = (15*0.3) + (20*0.5) + (30*0.2) = 20.5

crop 2 = (30*0.3) + (25*0.5) + (25*0.2) = 26.5

crop4 = (40*0.3) + (40*0.5) + (40*0.2) = 40

The second branch consist of the decision option therefore we will compare the profits

crop 1 = 31.5*\$1=\$31.5

crop2 = 20.5*\$1.5=\$30.75

crop 3 = 26.5*\$1.00=\$26.5

crop 4 = 40*\$0.50 = \$20

there fore crop 1 has maximum profits