Party World is a store selling party stuffs. One of its popular products for Halloween is Elvis wig. The Elvis wig is produced in Asia, so Party World has to make a single order well in advance of the upcoming season. Tony, the manager of the store estimates the following as his demand forecast

D Pr(D) F(D)

5,000 0.05 0.05

10,000 0.10 0.15

15,000 0.15 0.30

20,000 0.20 0.50

25,000 0.22 0.72

30,000 0.15 0.87

35,000 0.10 0.97

40,000 0.03 1

The Elvis wig retails for $15, Party World pays $6 per unit to its manufacturer in Asia. Leftover inventory can be sold to discounters for $2.

a) What order quantity maximizes Party World’s expected profit?

b) If Party World orders the quantity in part a), what is Party World’s expected fill rate?

c) If Party World orders the quantity in part a), then how many customers does Party World expect to turn away because of shortage?

d) If Party World orders the quantity in part a), then how many wigs can they expect to have to liquidate?

e) If Party World wants to have a 90% Cycle Service Level (CSL), then how many Elvis wigs should be ordered?