A cellphone store specializes in a popular and fancy cellphone. Assume that the store can only order cellphones from the manufacturer at the beginning of the month, and these cellphones become obsolete at the end of the month. The store promises its customers that next-day delivery is guaranteed if the cellphones are out of stock. In such cases, the store purchases the cellphone from an out-of-state retailer and has it delivered through an express service. Thus, when out of stock, the store loses the potential sale of a cellphone and pays for the shipping charge but maintains its good reputation.

- Retail price of the cellphone: $220
- Special delivery charge: $30
- Inventory holding cost per cellphone at the end of the month: $50
- Wholesale cost per cellphone: $100
- Monthly demand is discrete uniform between 17 to 20 cellphones (inclusive). That is, [tex]\text{Pr}[D = d] = \frac{1}{4}[/tex] for [tex]d = 17, 18, 19, 20[/tex].

Questions:
(a) If 18 cellphones are ordered at the beginning of a month, what are the expected overstock cost and the expected understock cost? What is the expected total cost?

(b) What is the optimal number of cellphones to order to minimize the expected total cost?

(c) Suppose now that the wholesaler has offered to provide 10 brand new phones for free to the store, regardless of the quantity ordered by the store. Should the store order additional phones? If yes, how many units should be ordered?