answer and explain all parts

Perdue supplies frozen chicken wing to the local grocery chain Shop Rite. The variable cost for Perdue is $200/box. Perdue sells it to Shop Rite at the price of $400/box. The retail price at Shop Rite is $700/box. Two weeks before the expiration date, any unsold chicken wing will be sold to a discount channel at the price of $100/box. In the current sales season, the chickenwing demand of Shop Rite can be 300, 350, 400, 450, 500 boxes, each with probability of 20%. You only need to consider the sales of the current season. There is only one chance to order for each season, therefore, this is a one shot decision. (1) How many boxes of chicken wings should Shop Rite Order? (2) In average, how many boxes will be sold through the discount channel? (3) What is the expected profit for Shop Rite? (4) If the supply chain is fully coordinated, what is the supply chain profit? (5) Keeping the $400/box wholesale price, Perdue want to propose a (lowest cost) buyback contract to coordinate the supply chain. What should be the buyback price? Please round to integer dollar value. (6) Please discuss the potential implementation issue of the buyback contract. (7) Please design an options contract that is equivalent to the buyback contract in (5). (8) Shop Rite makes a proposal to Perdue suggesting Perdue to reduce the whole sale price to $300/box. In exchange, Shop Rite is willing to share 10% of their revenue. Should Perdue accept this offer, i.e., does Perdue make more money? (9) What is the equivalent revenue sharing contract of the buyback contract in (5)? What is the problem with this contract? How to solve the