Consider the following problem. Demand: q = 100-p Retailer: marginal cost of selling r = 10 per unit Manufacturer: marginal cost of producing = 40 per unit Neither firm faces any competitor 1. Suppose the manufacturer owns the retailer. Write down the profit function of the vertically-integrated firm and solve for monopoly price, quantity, and total profit. 2. Suppose now that the retailer and the manufacturer are separate firms. The retailer will buy from the manufacturer at a unit price w (wholesale price). Write down the profit function of the retailer if it buys at w per unit, incurs the marginal cost of selling, and faces the same demand curve as before. Solve for the optimal price for the retailer and the quantity sold as functions of w.