Response to the following problem:
Brenton $oftware Publishing Company (BSP) offers its sales representatives a choice of three compensation plans based on how many universities adopt Brenton's new statistical software package. The three plans are as follows:
Plan 1: A fixed salary of $2000 per month.
Plan 2: A fixed salary of $1000 per month plus a commission of $300 for each university that adopts the statistical package.
Plan 3: A commission of $700 for each university that adopts the statistical package.
Ted Benson is a new sales representative for BSP and must decide which compensation plan to accept. Experienced sales representatives have told him that he can expect that up to six universities per month will adopt the software. Ted is free to change his compensation plan at the beginning of any month.
a. Construct a payoff table showing Ted's monthly compensation as a function of the compensation plan he chooses and the monthly adoptions.
b. Which plan should Ted choose if he uses the minimax regret criterion?
c. Suppose Ted believes that the following probabilities hold regarding monthly adoptions for his first month with the firm:
P(0 adoptions) = .10
P(1 adoption) = .15
P(2 adoptions) = .25
P(3 adoptions) = .20
P(4 adoptions) = .15
P(5 adoptions) = .10
P(6 adoptions) = .05
On the basis of these data, which compensation plan should Ted select for the upcoming month?