Smith and Jackson (SJ) sells an outdoor grill to Cusano’s Hardware Store. SJ’s wholesale price for the grill is $185. Cusano sells the grill for $250 and SJ’s variable cost per grill is $100. Suppose Cusano’s forecast for season sales can be described with a Normal distribution with mean 10 and standard deviation 5. Grills left over at the end of the season are sold at $62.5. (part c only!!)

a.     How many grills should Cusano order to maximize its own profit? (10 points)

ANS: Cusano’s discount price is (1-0.75)x 250 = 62.5. Cusano’s overage cost is Co = 185 -62.5 = 122.5. Cusano’s underage cost is Cu = 250 – 185 = 65. The critical ratio is 65 / (122.5 + 65) = 0.34667. From the Poisson Distribution Function Table F(6) = 0.23051 and F(7) = 0.35398, so the optimal order quantity is Q = 7.

b.    To maximize the supply chain’s total profit (SJ’s profit plus Cusano’s profit), how many grills should be shipped to Cusano’s hardware? (20 points)

ANS: The supply chain’s overage cost is Co = 100 – 62.5 = 37.5. The supply chain’s underage cost is Cu = 250 – 100 = 150. The critical ratio is 150 / (37.5 + 150) = 0.8000 From the Poisson Distribution Function Table F(10) = 0.73519 and F(11) = 0.82657, so the optimal order quantity is Q = 11.

c. (only need to solve this) Suppose SJ and Cusano agree on the following revenue sharing contract: the wholesale price is $80 (as opposed to $185 in the original contract) and the per-unit revenue of $250 is shared with SJ; that is, Cusano keeps $250(1-y) and SJ keeps $250y of the revenue per grill. To achieve the first-best profit in part b, what should y be?