In homework 9 , we solved a problem using a buy - back agreement as incentives in the supply chain. Suppose instead of a buy

In homework $9,$ we solved a problem using a buy$-$back agreement as incentives in the supply chain. Suppose instead of a buy$-$back agreement, there is a revenue sharing agreement between the retailer and manufacturer. The manufacturer offers the retailer a $\mathrm{10}\%$ discount. In return, the retailer keeps $\mathrm{90}\%$ of the profit for each unit sold and the manufacturer receives $\mathrm{10}\%$ of the profit for each unit sold. Below are the numbers we used in the class example and homework $\mathrm{9.}$ Please use these numbers and the revenue sharing agreement to calculate the expected profit for the manufacturer, expected profit for the retailer, and expected channel profit.

Manufacturer Retailer Consumer

C W

D: $\backslash$mu $=\mathrm{500}$; $\backslash$sigma $=\mathrm{100}$

c$=$$$\mathrm{12}$; w $=$ $$\mathrm{30}$; p $=$ $$\mathrm{100}$; unsold units get $$\mathrm{10}$ per unit.