Question 3: Supply Chain Coordination Universal Pass is a dealer of motorcycles in North Carolina. They order motorcycles from an oversea supplier. Consider one type of battery-operated motorcycle. The dealer purchases the motorcycles from the supplier at a wholesale price of $300 per unit and sells at a unit price of $499. It costs the supplier $200 to produce one such motorcycle. The quarterly demand and associated probabilities for this motorcycle based on past data are shown in the following table. a) How many of these motorcycles should the Universal Pass order every quarter if there is no supply-chain coordinating contract? What are the expected profits for Universal Pass and its supplier corresponding to this order quantity? b) Assume that Universal Pass and the supplier (not vertically integrated) are operating under the following revenue share contract: the supplier offers Universal Pass a wholesale price of $220 per unit; Universal Pass keeps 80% of the revenue and its supplier takes the rest of the revenue. If the dealer orders 330 motorcycles every quarter, what is the expected profits for Universal Pass and its supplier? What would be the best order quantity if Universal Pass accepts this contract? Suppose that Universal Pass orders this best order quantity, is it willing to accept the offer? c) What is the optimal order quantity for Universal Pass in a vertically integrated supply chain (i.e. Universal Pass and its supplier belongs to the same company)? What is the expected total profit for this vertically integrated supply chain? d) Assume that Universal Pass and its supplier (not vertically integrated) are operating under a buyback contract with the buyback price of $200 per unit, will the supply chain be coordinated with the wholesale price of $300 per unit? At what buy back price will the supply chain be coordinated? e) Assume that Universal Pass and its supplier (not vertically integrated) are operating under a buyback contract. Suppose that during the shipment of returning motorcycles, Universal Pass needs to pay additional inventory holding cost of $8 associated with each motorcycle. Suppose that the wholesale price is $300 per unit. Would Universal Pass expect a higher or lower buyback price compared with that in d)? Explain your