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

F=$120,000 ; c=$50 ; w=$75 ; s=$15 ; v=$19 ; p=$120;

The demand forecasting can be found as below:

D (units)	9,000	9,450	9,923	10,419	10,940	11,487
Prob	0.14	0.09	0.26	0.21	0.18	0.12

1. Calculate the manufacturer's marginal profit, manufacturer's marginal loss, distributor's marginal profit.
2. Calculate the expected profit of the retailer and the manufacturer for 6 above-mentioned demand scenarios. Then, conclude on which production quantity Q to maximize manufacturer's expected profit, which production quantity Q to maximize distributor's expected profit.