HW-512 Alibaba Co. carpet problem

The Ali Bab Co. is the only supplier of a particular type of Oriental carpet. The estimated demand for its carpets is Q = 110,000 - 500 P + 5 M where Q = number of carpets, P = price of carpets ($ per unit), and M = consumers' income per capital. The estimated average variable cost function for Ali Bab's carpets is AVC = 200 + 0.008Q, MC = 200 + 0.016Q Consumers' income per capital is expected to be $20,000 and total fixed cost is $100,000.
How many carpets should the firm produce in order to maximize profit?

What is the profit maximizing price of carpets?
What is the maximum amount of profit that the firm can earn from selling carpets


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