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$)$