Suppose that the demand curve for a monopolist is given by Q = 200 - P, and the marginal revenue function is MR = 200 - 2Q.The monopolist has a constant marginal and average total cost of $50 per unit (i.e. MC = AC = 50).Answer the following questions.YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT.(10 PTS)

a)Find the monopolist's profit-maximizing output and price

b)Calculate the monopolist's maximum profit.

c)Assume that the monopolist's per unit cost has changed to MC = AC = 100, calculate the new profit-maximizing output and price, and the new maximum profit.