Dior owns Louis Investigations, a private investigation company specializing in infidelity documentation for divorce cases. Dior charges $20,000 per divorce investigation. Dior must decide how many regular investigators to put on salary for next month. Each regular investigator can complete 1 divorce investigation in a month. Full time investigators receive $10,000 per month salary. Dior estimates that the number of divorce investigations next month is Divorce Investigations Probability 5 .3 6 .6 7 .1 If Dior does not schedule enough regular divorce investigators, then he hires off duty Los Angeles detectives but they charge $32,000 per divorce investigation. If Dior hires more regular investigators then he needs for divorce cases, he uses them for asset tracing which is valued at $12,000 per investigator per month.

a. What is the unit cost of understock and the unit cost of excess (overstock). Find the optimal percentile and the optimal number of regular investigators to hire for the month.

b. Write the expression for the expected payoff associated with this optimal strategy.