Pony Express Creations Inc. (www.pony-ex.com) is a manufacturer of party hats, primarily for the Halloween season. (80 percent of their yearly sales occur over a six-week period.) One of their popular products is the Elvis wig, complete with sideburns and metallic glasses. The Elvis wig is produced in China, so Pony Express must make a single order well in advance of the upcoming season. Ryan, the owner of Pony Express, expects demand to be 25,000 and the following is his entire demand forecast:

The Elvis wig retails for $25, but Pony Express's wholesale price is $12. Their production cost is $6. Leftover inventory can be sold to discounters for $2.50.
a. Suppose Pony Express orders 40,000 Elvis wigs. What is the chance they have to liquidate 10,000 or more wigs with a discounter?
b. What order quantity maximizes Pony Express's expected profit?
c. If Pony Express wants to have a 90 percent in-stock probability, then how many Elvis wigs should be ordered?
d. If Pony Express orders 50,000 units, then how many wigs can they expect to have to liquidate with discounters?
e. If Pony Express insists on a 100 percent in-stock probability for its customers, then what is its expected profit?

Transcribed Image Text:

F(Q) 0.0181 0.0914 0.2381 0.4335 0.6289 0.7852 0.8894 0.9489 0.9787 0.9919 0.9972 0.9991 0.9997 0.9999 1.0000 L(Q) 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 55,000 60,000 65,000 70,000 75,000 Prob( D-Q) 0.0181 0.0733 0.1467 0.1954 0.1954 0.1563 0.1042 0.0595 0.0298 0.0132 0.0053 0.0019 0.0006 0.0002 0.0001 20,000 15,091 10,548 6,738 3,906 2,050 976 423 168 61 21