The demand distribution for one of the snow jack designs is as follows:

Demand (D)	8,000	10,000	12,000	14,000	16,000	18,000
Probability	0.11	0.11	0.28	0.22	0.18	0.1

For the buy-back contract discussed in the class, the parameters are as follows:

Retail Price	$125
Salvage Price	$20
Variable Production Cost	$35
Fixed Production Cost	$100,000

For the revenue sharing contract discussed in the class, the parameters are as follows:

Retail Price	$125
Salvage Value	$20
Variable Production Cost	$35
Fixed Production Cost	$100,000

1. Use the scenario approach to find the optimal order quantity and expected profit for the retailer under a wholesale-price only contract. W= $80, P= $125, S=$20, fixed set-up cost F = $100,000. This problem is the same as the example discussed in the class. Please calculate the retailers and the manufacturers profits with the above parameters and compare with the answers in the slides, and see if the manufacture salvage the buy-back items or not for the answers in the slides. The purpose is to verify you set up the spread sheets correctly.
2. Find the optimal order quantity for the retailer under the following two new buy-back contracts: (1) w=$71 and b=$50; (2) w=$89 and b=$75. Calculate the expected profits for the retailer, the manufacturer, and the whole supply chain under each contract.
3. Find the optimal order quantity for the retailer under the following two new revenue sharing contracts: (1) w=24 and f=0.4; (2) w=21 and f=0.6. The revenue sharing rate, f, is the proportion paid to the manufacturer. Calculate the expected profits for the retailer, the manufacturer, and the whole supply chain under each contract.
4. * Find the underage cost, the overage cost, and the optimal order quantity under each scenario in the above questions.
5. * The manufacturer may induce the retailer to increase the order quantity by lowering the wholesale price. Under a wholesale-price only contract, what wholesale price is needed to induce the retailer to order a quantity that is optimal for the system (i.e., manufacturer and retailer). What will be the problem with this wholesale price?