The total revenue curve of a firm is R(x) = 32 · 5x – 12x 2 and its average cost A(x) = 1 x 2 – 13x + 20 + 200; where x is the firm’s output. 30 x A) Derive an expression, Π (x), for the firm’s profit...

The total revenue curve of a firm is R(x) = 32·5x – 12x²and its
average cost A(x) =1x² – 13x + 20 +200;
where x is the firm’s output.
                               30                           x                                                             A) Derive an expression, Π (x),  for the firm’s profit function.

B) Is the rate of change of profit increasing or decreasing
     when the output level of the firm is x = 10 and x = 30?

c) Determine the level of output for which profit is maximized.

(d). What is the maximum profit.