Consider a supplier selling a seasonal product to a retailer at the wholesale price of $75. It costs the supplier $45 to procure the good. The retailer sells the good to the end-customer at a price of $125. Assuming the salvage value of the good is zero and the seasonal demand for the product is normally distributed with mean 100 and standard deviation 20, answer the following:
a. What is the optimal order quantity for the retailer in the absence of a coordinated contract?
b. What is the profit for the retailer?
c. What is the profit for the supplier?
d. What is the optimal order quantity under the supply-chain coordinated case?
e. What is the supply chain profit of the coordinated case?
f. How much is the supply chain losing with the wholesale price contract compared to the coordinated case?
g. What is the optimal buyback price the supplier needs to offer to the retailer if she wants to extract as much supply chain profit as possible assuming the wholesale price remains at $75?