Jewelry Jacks is a store selling jewelry items. One of its popular products for summer is the hoop earring. The Earring is produced in a foreign country, so Jewelry Jacks has to make a single order well in advance of the upcoming season. Jack, 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 0.16 0.31

20,000 0.20 0.51

25,000 0.22 0.73

30,000 0.14 0.87

35,000 0.10 0.97

40,000 0.03 1

The earring-hoop retails for $12, Jewelry Jacks pays $6 per unit to its manufacturer in a foreign nation. Leftover inventory can be sold to discounters for $2.50.

1. What order quantity maximizes Jewelry Jack's expected profit?

2. If Jewelry Jack orders the quantity in part a), what is Jewelry Jack's expected fill rate?