A retail outlet sells holiday decorations for $10 per bag. The cost of the product is $8 per bag. Any units not sold during the selling season can be sold for $5 a bag at the end of the season. Assume that demand for these decorations is normally distributed with a mean of 500 and standard deviation of 100 bags.
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?
c. Suppose at the end of the selling season, the decorations have no value and have to be disposed of at a cost of $0.10 per bag. Now what is the optimal order quantity?
d. To keep customers happy and coming back, the owner of the store feels that stock-outs should be avoided. What is the your recommended order quantity if the owner is willing to tolerate only a 0.15 probability of a stock-out?
e. Using your answer to part (d) what is the goodwill cost you are assigning to a stock-out?