Case Scenario:
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 productivities for each vegetable in dry, moderate, and damp weather and also lists the price per bushel that the cannery has offered for each crop:
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Approximate Yield (bushels per acre)
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Weather
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corn
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tomatoes
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beets
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asparagus
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cauliflower
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Dry
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20
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10
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15
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30
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40
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Moderate
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35
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20
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20
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25
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40
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Damp
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40
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10
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30
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20
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40
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price per bushel
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$1.00
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$2.00
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$1.50
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$1.00
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0.5
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1) Construct the payoff table for the farmer’s decision. For the payoff measure use the approximate total cash receipts when the crop is sold
2) Identify any inadmissible acts and eliminate them from the payoff table.
3) 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