Problem:
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:
Required:
Question 1) 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).
Question 2) For this payoff table find Jim's optimal decision using: (1) the conservative approach, (2) minimax regret approach and (3) the optimistic approach.
Question 3) 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? Hint: 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
Solve the problem and show all work.