NEED 6-9!!!!

Tyson Co supplies frozen chicken wing to the local grocery chain Price Chopper. The variable cost for Tyson is $200/box. Tyson sells it to Price Chopper at the price of $400/box. The retail price at Price Chopper 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 chicken-wing demand of Price Chopper 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 Price Chopper Order?
2. In average, how many boxes will be sold through the discount channel?
3. What is the expected profit for Price Chopper?
4. If the supply chain is fully coordinated, what is the supply chain profit?
5. Keeping the $400/box wholesale price, Tyson 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. Price Chopper makes a proposal to Tyson suggesting Tyson to reduce the whole sale price to $300/box. In exchange, Price Chopper is willing to share 10% of their revenue. Should Tyson accept this offer, i.e., does Tyson make more money?
9. What is the theoretically equivalent revenue sharing contract of the buyback contract in (5)? What is the problem with this contract? How to solve the problem?