Q1) During the Final Four, demand for basketball jerseys is uniformly distributed with minimum demand a = 100 and maximum demand b = 500. Each jersey costs $30. The selling price is $40 per jersey.

(a) How many jerseys should be ordered according to the newsvendor model? (5 points)

(b) Suppose instead that the demand for basketball jerseys is normally distributed with mean 1000 and standard deviation 300. In addition, suppose that the unsold jerseys can be sold off at half price. How many jerseys should be ordered now? Use the table below to get the z-value for the critical ratio you compute. (Hint: The overage cost is affected in a similar way as in the buy-back contract we saw in class.) (5 points)

Critical Ratio z 0.25 -0.67 0.5 0 0.57 0.18 0.8 0.84

Q2) As owner of Catch-of-the-Day Fish Shop, you can purchase fresh fish at $18 per crate each morning from the Walton Fish Market. During the day, you sell crates of fish to local restaurants for $120 each. Coupled with the perishable nature of your product, your integrity as a quality supplier requires you to dispose of each unsold crate at the end of the day. Your cost of disposal is $2 per crate. You have a problem, however, because you do not know how many crates your customers will order each day. To address this problem, you have collected several days' worth of demand data shown in the table below.

Determine the optimal number of crates you should purchase each morning according to the newsvendor model. Demand 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Frequency 0 0 0 1 3 2 5 1 6 7 6 8 5 4 1 3

Q3) A print house prints business newspapers for its customer, Old York Times (OYT). The cost of printing each newspaper for the print house is $0.4 and it sells newspapers to OYT at $0.7 per copy. OYT then sells those newspapers to customers at $1 per copy.

(a) What is the newsvendor critical ratio for OYT?

(b) What is the newsvendor critical ratio for the centralized system, i.e. when the print house and OYT act as one company?

(c) What buyback price should the print house offer OYT to coordinate the supply chain, i.e. maximize the total supply chain profit?