Question 1 (30 points): Joe, a Supply Chain Masters student at York University is planning to sell Tshirts with logos of the two competing Grey Cup teams at the upcoming Grey Cup in Hamilton. Joe plans to have the shirts made by a local producer, who produces them at $10 and will sell them for $18 each. Joe is planning to sell the T-shirts for $25. If any left at the end of the season, he will dispose them by donating to a charity. The past experience indicates that the demand can reasonably be estimated with the following distribution: Demand (units) Probability 250 0.10 300 0.15 350 0.15 400 0.35 450 0.15 500 0.10 a) How many T-shirts should Joe order? b) What are the resulting profits for Joe and the producer? c) If the system is managed by the producer in an integrated way, what would be the quantity ordered and the total supply chain profit? d) How can the producer devise a buy-back contract that coordinates the system? What would be the respective profits? e) Devise a revenue sharing contract in which the producer sells the T-shirts for $5 each. Find the revenue share and compute the respective profits.