Imagine a two$-$firm supply chain that consists of a supplier and a retailer. The supplier has a marginal cost c $=$$$40$ and a wholesale price w $=$ $$60.$ The retailer is looking to sell its product at p $=$ $$100$; at this price point, demand over the lifespan of the product is distributed normally with mean $200$ and standard deviation of $10.$ a$)$ What is the expected profit for the supplier and the retailer assuming each of them maximizes their own profit?