Consider a supply chain with the manufacturer, the retailer and end-users, using a buy-back contract, as below cost-benefit & demand forecasting details:

F=$120,000 ; c=$30 ; w=$75 ; b=$50 ; p=$122 ; s=$15;

Demand	1,800	1,920	2,040	2,160
Probability	26%	27%	29%	18%

1. Calculate the retailer’s marginal profit, retailer’s marginal loss, manufacturer’s marginal profit.
2. Calculate the expected profit of the retailer and the manufacturer for 4 above-mentioned demand scenarios. Then, conclude on which production quantity Q to maximize manufacturer’s expected profit, which production quantity Q to maximize retailer’s expected profit.