econplease answer with complete solutions. ty!

Superior Co. is the only supplier of a particular type of Persian carpets. The estimated demand for its carpets is Q = 112,000 - 500P + 5M where Q = number of carpets, P = price of carpets (dollars per unit) M = consumers' income per capita. The estimated average variable cost function for Superior carpets is AVC - 200 - 0.0120 + 0.00000202 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 in order to maximize profit? (10 pts) b. What is the profit-maximizing price of carpets? (2 pts) c. What is the maximum amount of profit that the firm can earn selling carpets? (4 pts)