The demand function of a company is Q = 20 - 0.4p.

(1) Please derive its inverse demand function, i.e., express p as a function of Q. (Q stands for quantity demanded, and p is the market price).

(2) What is the marginal revenue function?

(3) If the marginal cost of the company is $10. What is the optimal quantity that maximizes its profit? What is the maximized profit?

(5) Suppose the marginal cost decreases to $8. What is the optimal quantity? Does it increase, decrease, or stay the same? In the same diagram from (5), graph the change of marginal cost function, optimal quantity, and optimal price (if there is any change at all).

6. Suppose that you can sell as much of a product as you like at $92 per unit. Your marginal cost (MC) for producing the Qth unit is given by: MC=10Q. If fixed costs are $350, what is the optimal output level?

7. Suppose a firm has as its total cost function: TC = 24 + 2Q2, and its output can be sold at $44 per unit. Using calculus to find the firm's profit-maximizing output. What is the maximized profit?