A monopolist faces the following demand and total cost functions:

Q= 65 - 1/2P

TC = Q^2+10Q + 50

(a) Calculate the profit maximizing output and price of the monopolist. Calculate the resulting profit.

(b) Suppose the government imposes an excise tax of $30 on the production and sale of the product. Calculate the resulting optimal profit maximizing output and price for the monopolist. Also determine the level of profit.

(c) If the government's objective is to generate the maximum possible tax revenue from the monopolist, what excise tax rate should the government impose on the monopolist? Calculate the resulting optimal output, and price of the monopolist as well as government's tax revenue.