Consider the following demand scenario: Quantity 2,000 2,100 2,200 2,300 2,400 2,500 2,600 2,700 Probability 3% 8% 15% 30% 17% 12% 10% 5% Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to end customers for $50/unit during season, unsold units are sold for for $10/unit after season. a. What is the system optimal production quantity and expected profit under global optimization? b. Suppose the manufacturer is make-to-order; that is, the timing of events is as follows: The distributor orders before it receives demand from end customers. . The manufacturer produces the amount ordered by the distributor. Customer demand is observed. i. Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and distributor? Consider the following demand scenario: Quantity 2,000 2,100 2,200 2,300 2,400 2,500 2,600 2,700 Probability 3% 8% 15% 30% 17% 12% 10% 5% Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to end customers for $50/unit during season, unsold units are sold for for $10/unit after season. a. What is the system optimal production quantity and expected profit under global optimization? b. Suppose the manufacturer is make-to-order; that is, the timing of events is as follows: The distributor orders before it receives demand from end customers. . The manufacturer produces the amount ordered by the distributor. Customer demand is observed. i. Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and distributor