Question 3:

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 manufacturers marginal profit, manufacturers marginal loss, distributors 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 manufacturers expected profit, which production quantity Q to maximize distributors expected profit.