Consider the following demand scenario: The variable production cost is $45/ unit and the fixed cost is $125,000. The product is sold to end customers for $145/ unit during the season and any unsold units are sold for $20/ unit after the season. In a buy back scenario, the manufacturer will buy back units at $55/ unit. Also, in a payback scenario, the retailer will pay $15 for each unit it does not purchase. In both the payback and buy back scenarios, the manufacturer sells the product for $75.00. a) What is the system optimal production quantity and expected profit under global optimization? b) What is the system optimal production quantity and expected profit under a payback scenario? What is the profit for the retailer and for the manufacturer? c) What is the system optimal production quantity and expected profit under a buyback scenario? What is the profit for the retailer and for the manufacturer? d) Provide the results of your analyses supporting your answers to parts a) through c)