a. Firm K is a leading maker of water-proof outerwear. During the winter months, demand for its main line of water-proof coats is given by:
P = 800 - .15Q,
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 = 175,000 + 300Q + .1Q2
(Leasing the plant accounts for almost all of the $175,000 fixed 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?
b. From time to time corporate customers place “special” orders for customized versions of Firm K’s coat. Because they command premium prices, corporate orders generate an average contribution of $200 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 K has just received an unexpected corporate order for 200 coats but has unused capacity to produce only 100.
What would you recommend? In general, can you suggest ways to free up capacity in the winter?
c. Because of rival firms’ successes in developing and selling comparable (sometimes superior) coats and outerwear, Firm K’s winter demand permanently falls to P = 600 - .2Q. What is the firm’s optimal operating policy during the next three winter months? When its plant lease expires in June?