2. (20 points). Firm K is a leading maker of light-weight, water-proof outerwear. During the winter months, demand for its main line of water-proof coats is given by: P = 800 0.2Q, where P denotes price in dollars and Q is quantity of units sold per month. The firm produces coats in a single plant (which it leases by the year). The total monthly cost of producing these coats is estimated to be: C = 150, 000 + 400Q. Leasing the plant accounts for almost all of the $150,000 fixed cost. What is the firm's marginal cost? Find the firm's profit-maximizing output and price. If the firm's other outerwear products generate $50,000 in contribution, what is the firm's total monthly profit? (a) From time to time corporate customers place special orders for customized versions of Firm K's raincoat. Corporate orders generate an average contribution of $100 per coat. Firm K tends to receive these orders at short notice usually during the winter when its factory is operating with little unused capacity. Firm 1 K has just received an unexpected corporate order for up to 300 coats but has unused capacity to produce only 200. One manager recommends delivering 200 coats (The client would still be satisfied with 200 coats). A second manager argues for cutting back production of standard coats (by 100) to fill the full corporate order. Who is right? Explain carefully. In general, can you suggest any other ways to free up capacity in the winter?