Revisit the setting depicted in the note $$Channel Coordination Using Contracts.$$ Recall that we have a Retail Price of $$100,$ Production Cost of $$45,$ and Salvage Value of $$5.$ To simplify the problem assume that demand is equally likely to be exactly $1,2,3,4,$ or $5$ units and use the models in the CoordinationDiscrete.xlxs spreadsheet. Note that when the chain is coordinated the retailer prefers to order $3$ units and total profit for the chain will be $$108.$

A$)$ State terms for a contract with a fixed fee that coordinates the chain and leaves an expected profit level of $$10$ for the retailer. $(10$ Points$)$

B$)$ Find two different sets of terms for a Buy$-$back contract that coordinates the chain, and specify the profit levels for the Manufacturer and Retailer in each case. $(10$ Points$)$

C$)$ Find terms for a Revenue Sharing contract that coordinates the supply chain and leaves $($roughly$)$ $$10$ as expected profit for the Manufacturer. $(10$ Points$)$