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. Use Excel to conduct the following analyses:
a. Compute the monthly salary payoff table for Jim. Hint: There are three decision alternatives (salary plans) and seven states of nature (the number of houses sold monthly).
b. For this payoff table find Jim's optimal decision using:
(1) The conservative approach,
(2) Minimax regret approach.
c. Suppose that during the past year the following is Jim's distribution of home sales. If one assumes that this a typical distribution for Jim's monthly sales, which salary plan should Jim select? Use the relative frequency approach to assign probabilities to each state of nature.
Home Sales 0 1 2 3 4 5 6
Number of Months 1 2 1 2 1 3 2