The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. The estimated demand for its
Q = 112,000 − 500P + 5M
where Q = number of carpets, P = price of carpets (dollars per unit), and M = consumers' income per capita. The estimated average variable cost function for Ali Baba's carpets is AVC = 200 − 0.012Q + 0.000002Q2
Consumers' income per capita is expected to be $20,000 and total fixed cost is $100,000. a. How many carpets should the firm produce to maximize profit? b. What is the profit-maximizing price of carpets? c. What is the maximum amount of profit that the firm can earn selling carpets?