The total Revenue curve of a firm is R(q) = 40q -12q^2 and its average cost A(q) = 1/30q^2 – 12.85q XXXXXXXXXX/q, where q is the firm’s output. (i) Derive an expression C(q) for the firm’s total cost...

The total Revenue curve of a firm is R(q) = 40q -12q^2 and its average cost A(q) = 1/30q^2 – 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 for the firm’s profit function.

(iii) Is the rate of change of profit increasing or decreasing when the output 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?