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# Computing a Payoff Table and Finding an Optimal Decision Using Given Data

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Jim has been employed at Gold Key Realty at a salary of \$2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to \$2,500 per month; (2) a base salary of \$1,000 plus \$600 per house sold; or, (3) a straight commission of \$1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month.

a) Compute the monthly salary payoff table for Jim. Hint: The decision alternatives are whether to choose plan 1, 2 or 3.
Hint: The states of nature are the number of homes sold (0,1,2,3,4,5 or 6)

b) For this payoff table find Jim's optimal decision using: (1) the conservative approach, (2) minimax regret approach and (3) optimistic approach

c) Suppose that during the past year the following is Jim's distribution of home sales. If one assumes that this is a typical distribution for Jim's monthly sales, which salary plan should Jim select?
Hint: Find the best decision using the EV approach.
Use the relative frequency method for determining the probabilities.
For Example: P(0)=1/12 and P(5)=3/12

Home Sales Number of Months
0 ................................1
1 ...............................2
2 .................................1
3 ...............................2
4 ...............................1
5 .............................3
6 .............................2

https://brainmass.com/math/probability/591841

#### Solution Summary

The solution gives deailed steps on computing payoff table, finding optimal decision using: (1) the conservative approach, (2) minimax regret approach, (3) optimistic approach and (4) EV approach.

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