Problem $5$

$(15$ marks$)$

Jill has been employed at ABC Realty with a salary of $$2,000$ per month during the

past year. Because Jill is considered to be a top salesperson, the manager of ABC is

offering her 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, Jill has sold up to $6$ homes

in a month.

a$.$ Compute the monthly salary payoff table for Jill.

b$.$ For this payoff table, find Jill's optimal decision using: $(1)$ the conservative

approach, $(2)$ minimax regret approach.

c$.$ Suppose that the following is Jill's distribution of home sales during the past

year. If one assumes that this a typical distribution for Jill's monthly sales,

which salary plan should Jill select?