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?

(4) Graph the marginal cost and marginal revenue function in (Q, p) space. Indicate their intercepts on each axis. Indicate the optimal output and price in the graph.