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Quantitative Decision Making with a Payoff Table

Decision Making Process

5-11 Rich Sod is a farmer who intends to sign a contract to provide a company with his entire crop. Rich must choose to produce one of the following five vegetables: corn, tomatoes, beets, asparagus or cauliflower. Rich will plant his entire 1,000 acres with the selected crop. The yields of these vegetables will be affected by the weather to varying degrees. The following table indicates that approximate productiveness for each vegetable in dry, moderate, and damp weather and also lists the price per bushel that the cannery has offered for each crop:

Approximate Yield (bushels per acre)
Weather corn tomatoes beets asparagus cauliflower
Dry 20 10 15 30 40
Moderate 35 20 20 25 40
Damp 40 10 30 20 40

price per bushel $1.00 $2.00 $1.50 $1.00 0.5

A) Construct the payoff table for the farmer's decision. For the payoff measure use the approximate total cash receipts when the crop is sold
B) Identify any inadmissible acts and eliminate them from the payoff table.
C) Suppose that the following probabilities have been assigned to the types of weather, calculate the expected payoff for each act. Then, identify the act that has the maximum expected payoff.

Weather Probability

Dry .3
Moderate .5
Damp .2

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Solution Summary

The solution helps determine a farmer's best course of action by using payoff tables.