The demand curve of a firm is p = XXXXXXXXXX21q and its total cost is C(q) = 2q 3 -66q 2 +600q XXXXXXXXXXwhere q is the output of the firm (in thousand) (i) Derive an expression R(q) for the firm's...

The demand curve of a firm is p = 1200 - 21q and its total cost is C(q) = 2q³-66q
²
+600q + 1000 where q is the output of the firm (in thousand)

(i) Derive an expression R(q) for the firm's revenue function

(ii) Derive an expression (q ) for the firm's profit function

(iii) Is the rate of exchange of profit increasing or decreasing when the output level of the firm is 10,000 units?

(iv) Determine the level of ouput at whihc profit is maximised