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?

 

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

Answer rating: 100% (QA)

If ny exress urhses 40000 units then it hs t liquidte 10000 r mre units rvided if the demnd is 30000 ... View the full answer