The total revenue curve of a firm is R(q) = 40q − 12q2  and its average cost A(q) = 1/30 q2 − 12.85q + 20 +400/q, where q is the firm's output. i. Derive an expression C(q) for the firm's total cost function.ii. Derive an expression Π(q) for the firm's profit function.iii. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?iv. Determine the level of output for which the firm's profit is maximized.v. What is the firm's maximum profit?

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Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q +…

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Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

A: Total revenue, R (q) = 40q - 12q2  Average cost, A(q) = 1/30q2 - 12.85q +20 + 400/q

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Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q…

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