Further, suppose that the cost function for providing minutes on the phone is given by c(x) = x2. The profit function is given by π = k(x*) - C(x*), where x* is the optimal consumption given the pricing scheme solved in the previous exercise. What are the optimal price choices for the firm under linear or flat-fee pricing if all customers were of type 1? Write down the profit function for each pricing scheme. Use a spreadsheet application (like Microsoft Excel) to solve for the price that maximizes the profit by trying various prices until you find the price yielding the highest profits. Which pricing scheme provides greater profits? Now try the same exercise assuming all customers are of type 2. Which pricing scheme now provides the greatest profits? How do you think the answer would change if the phone company believed they would have customers of both types?