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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 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 Crop 1 Crop 2 Crop 3 Crop 4

Dry 20 15 30 40

Moderate 35 20 25 40

Damp 40 30 25 40

Net income/bushel $1.00 $1.50 $1.00 $0.50

After referring to historical meteorological records, Dwight also estimated the following probabilities for the weather during the growing season:

Dry 0.3

Moderate 0.5

Damp 0.2

Required:

1. Construct a decision tree and use Bayes deicison fule to determine which crop to grow?

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Answers (1)
  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
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