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# Demand function , profit fuction

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Acme Coffee Bean Company sells coffee beans to both retail grocery chains and commercial users (e.g., coffee shops, vending companies, etc.). The demand function for each of these markets is:

Retail grocery chains: P1 = 180 - 8Q1
Commercial users: P2 = 100 - 4Q2

where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Acme's total cost function (which includes a "normal" return to the owners) for coffee is:
TC = 50 + 20(Q1 + Q2)

(a) Determine Acme's total profit function.
(b) Assuming that Acme is effectively able to charge different prices in the two markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Acme's total profit under this condition?
(c) Assuming that Acme is required to charge the same price in each market, what are the profit-maximizing price and output levels? What is Acme's total profit under this condition?