Question: Consider Happy Henry's car dealer described in Problem.

a. How many EX123s should Happy Henry's purchase to satisfy all the demand over a three-month interval with probability .95?

b. How many cars should be purchased if the goal is to satisfy 95 percent of the demands?

Problem: Happy Henry's car dealer sells an imported car called the EX123. Once every three months, a shipment of the cars is made to Happy Henry's. Emergency shipments can be made between these three-month intervals to resupply the cars when inventory falls short of demand. The emergency shipments require two weeks, and buyers are willing to wait this long for the cars, but will generally go elsewhere before the next three-month shipment is due. From experience, it appears that the demand for the EX123 over a three-month interval is normally distributed with a mean of 60 and a variance of 36. The cost of holding an EX123 for one year is $500. Emergency shipments cost $250 per car over and above normal shipping costs.

a. How many cars should Happy Henry's be purchasing every three months?

b. Repeat the calculations, assuming that excess demands are back-ordered from one three-month period to the next. Assume a loss-of-goodwill cost of $100 for customers having to wait until the next three-month period and a cost of $50 per customer for bookkeeping expenses.

c. Repeat the calculations, assuming that when Happy Henry's is out of stock of EX123s, the customer will purchase the car elsewhere. In this case, assume that the cars cost Henry an average of $10,000 and sell for an average of $13,500. Ignore loss-of-goodwill costs for this calculation.