Amelie is a winemaker in France. GoodWine is one of her retail partners in the US. GoodWine receives one delivery from Amelie each year before the summer season. GoodWine pays Amelie$75 per bottle and retails them for $100. Total production, shipping, and labor cost is $50 per bottle for Amelie. After the summer season, GoodWine sells any leftover bottles for $35 each. GoodWines marketing team believes that this years demand for French wine can be approximated by a uniform distribution between 50 and 250.

(a) What is GoodWines optimal order quantity? What is the expected profit for GoodWine? What is the expected profit for Amelie? What is the total profit of this supply chain?

(b) What is the integrated supply chains optimal order quantity? What is the total profit of the integrated supply chain?

(c) Amelie and GoodWine are trying to form a revenue sharing contract. Let f be the upfront fee which is $45 per bottle and be the revenue sharing percentage for GoodWine. What makes the chain perfectly coordinated? What is Amelies expected profit? What is GoodWines expected profit?

(d) Fix the wholesale price at $75. What would be the buy-back price that perfectly coordinates the supply chain? What is Amelies expected profit? What is GoodWines expected profit?

(e) Which contract between the revenue-sharing contract from (d) and buy-back contract from (e) would Amelie prefer? Explain why both quantitatively and qualitatively.