You and a friend get together to start a business, based on your friend's patent of a new and better ice cream scoop. Because you have the patent, you are the only producer of this product. You are in charge of marketing. Your research has led you to conclude that the demand function for your ice cream scoop is
Q = 200 - 4P
and the cost function is
TC = 9 + Q^2
What are your profit maximizing price and quantity? What profits will you make?