Consider a monopoly market with a demand function for which quantity demanded depends not only on price p but also on the amount of advertising the firm does, A, measured in dollars as are other costs. The specific form of this function is Q= (20-p)(1+0.1A-0.01A²). The firm's cost function is C(Q,A)=10Q+15+A.

(a) What is the firm's (unmaximized) profit function II(Q, A)?

(b) What are the first-order necessary conditions for a pair of values Q>0 and A>0 to maximize monopoly profit?

(c) Use your part-b conditions to solve for the profit-maximizing values of Q and A, and then use these to determine the market price p, the maximized profit level pi, and the associated amount of consumer surplus.