Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For

Question

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
Using
COnstruct a decision tree and use Bayes deicison fule to determine which crop to grow

Explanation / Answer

PS: Please rate the answer I'll provide you the answer but I'll leave the writing of decision tree to yourself. (Takes lot of time) Expected payoffs Crop 1: (20 * 0.3 + 35 * 0.5 + 40 * 0.2) * $1.00 = $31.50 Crop 2: (15 * 0.3 + 20 * 0.5 + 30 * 0.2) * $1.50 = $30.75 Crop 3: (30 * 0.3 + 25 * 0.5 + 25 * 0.2) * $1.10 = $26.50 Crop 4: (40 * 0.3 + 40 * 0.5 + 40 * 0.2) * $0.50 = $20.00 Dwight Moody should choose crop 1 with $31.50 payoff

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