An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 36

A retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit. All units not sold during the regular season are sold for half the retail price in an end-of-season clearance sale. Assume that demand for the product is uniformly distributed between 200 and 800.
a. What is the recommended order quantity?
b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? That is, what is the probability of a stockout using your order quantity in part (a)?
c. To keep customers happy and returning to the store later, the owner feels that stockouts should be avoided if at all possible. What is your recommended order quantity if the owner is willing to tolerate a 0.15 probability of a stockout?
d. Using your answer to part (c), what is the goodwill cost you are assigning to a stockout?