4. A jewelry shop procures a ring at $20 each and sells it at $80 each. Weekly demands for the ring over the past 20 weeks are as follows. Demand 51 52 53 54 55 56 57 58 59 60 Frequency 01 2 3 4 3 2 2 2 1 a. (5 pts) What are the under-stocking and over-stocking costs for the shop? b. (3 pts) What is the newsvendor critical ratio? c. (10 pts) How many rings per week should the shop order? d. (5 pts) Suppose that the weekly demand is uniformly distributed between 40 and 80. How many rings per week should the shop order? e. (5 pts) Suppose that the jewelry shop (Retailer) procures the ring from J&S company (Supplier). The supplier produces the ring at the cost of $10 each and sells it to the jewelry shop at the wholesale price of $20 each. The jewelry shop sells the ring at $80 each. Weekly demands for the ring over the past 20 weeks are given in the table above. If the two companies are merged into one, what are the critical ratio and the optimal production quantity? f. (6 pts) All the price data remain the same as in part e. Suppose that J&S company (Supplier) would like to offer a buyback contract to the jewelry shop (Retailer) to achieve the supply chain coordination. What should the buyback price be?