The total revenue curve of a firm is R(q) = 40q − 12q² and its  average cost A(q) = 1/30q² − 12.85q + 20 + 400/q ,where q is the firms output.

i. Derive an expression C(q) for the firms total cost function.

ii. Derive an expression Π(q) for the firms profit function.

iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units?

iv. Determine the level of output for which the firms profit is maximized.

v. What is the firmss maximum profit?