4. A firm has the cost C(q) = %qa 7q* + 111q + 50 and demand q = 100 - p functions. a. Write out the revenue function, R(q), in terms of q. [Hint: revenue is price * quantity]. b. Write out the profit function, P(q), in terms of q. c. Find the profit maximizing level of output, g*. [Hint: use the second derivative test] d. Find revenue R(q*). e. Find the cost C(q*). f. Find the maximum profit P(gq*). 5. Given a firm has revenue R(q) = 15q 0.5g? and cost C(q) = q> 13.5% + 50q + 40. a. Find Profit, P(q), in terms of q. [Recall: P =R(q) C(q)] b. Determine the quantity where the profit is maximized. [Hint: use the second derivative test] . What is the maximum profit at the quantity you found in part (b)