Problem 1: (8 Points) A farmer in Georgia must decide which crop to plant next y
ID: 428540 • Letter: P
Question
Problem 1: (8 Points) A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop, given the two possible results on the trade bill, is shown in the following payoff table Trade Bill Crop Corn Peanuts Soybeans Pass Fail S35,000 8,000 12,000 20,000 18,000 22,000 Determine the best crop to plant, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz (use a-0.4) e. Equal likelihoodExplanation / Answer
This criterion is very optimistic. “The decision maker will select the decision that will result in the maximum of the maximum payoff.” (Taylor, 2013) The selections for the farmer for this maximum payoff are under the category Pass. Of the three maximum payoffs, the maximum is $35,000. The best decision for the farmer would be to plant Corn for a $35,000 payoff.
This criterion is pessimistic. “The decision maker will select the decision that will reflect the maximum of the minimum payoffs. For each decision alternative, the decision maker assumes that the minimum payoff will occur.” (Taylor, 2013) The selections for the farmer for this maximum payoff are under the category Fail. Of the three minimum payoffs the maximum is $20,000. The best decision for the farmer would be to plant the Soybeans for a $20,000 payoff.
“With this decision criterion, the decision maker attempts to avoid regret by selection the decision alternative that minimizes the maximum regret.” (Taylor, 2013)
Pass Fail
$35,000 - $35,000 = $0 $20,000 - $8,000 = $12,000
$35,000 - $18,000 = $17,000 $20,000 - $12,000 = $8,000
$35,000 - $22,000 = $13,000 $20,000 - $20,000 = $0
Trade Bill
Crop Pass Fail
Corn $ 0 $ 12,000
Peanuts 17,000 8,000
Soybeans 0
The farmer will experience the least amount of regret by planting the Corn.
Under this decision criterion, “the decision maker is neither totally optimistic nor totally pessimistic. The decision payoffs are weighed by a coefficient of optimism, a measure of the decision maker’s optimism. ” (Taylor, 2013) When a = 1.0 it yields optimism. When a = 0 it yields pessimism.
Corn $35,000(.4) + $8,000(.6) = $18,800
Peanuts $18,000(.4) + $12,000(.6) = $14400
The farmer will plant the Soybeans for the maximum weighed value.
“Weights each state of nature equally, thus assuming that the states of nature are equally likely to occur. As with the Hurwicz criterion, we select the decision that has the maximum weighted values.” (Taylor, 2013)
Each value is assigned a weight of .50.
Peanuts $18,000(.5) + $12,000(.5) = $15,000
The farmer will plant the Corn for the maximum weighted value.