In Gomorrah, New Jersey, there is only one newspaper, the Daily Calumny. The demand for the paper depends on the price and the amount of scandal reported. The demand function is Q =15S^1/2p-3, where Q is the number of issues sold per day, S is the number of column inches of scandal reported in the paper, and P is the price. Scandals are not a scare commodity in Gomorrah. However, it takes resources to write, edit, and print stories of scandal. The cost of reporting S units of scandal is $10S. These costs are independent of the number of papers sold. In addition it costs money to print and deliver the paper. These cost $.10 per copy and the cost per unit is independent of the amount of scandal reported in the paper. Therefore the total cost of printing Q copies of the paper with S column inches of scandals is $10S + .10Q.

1. Calculate the price elasticity of demand for the Daily Calumny. _____ Does the price elasticity depend on the amount of scandal reported? ____ Is the price elasticity constant over all prices? ________
2. Remember that MR = P (1 + 1/). To maximize profits, the Daily Calumny will set marginal revenue equal to marginal cost. Solve for the profit-maximizing price of the Calumny to charge per newspaper ________ When the newspaper charges this price, the difference between the price and the marginal cost of printing and delivering each newspaper is _______
3. If the Daily Calumny charges the profit-maximizing price and prints 100 column inches of scandal. How many copies would it sell? (Round to the nearest integer) _____ Write a general expression for the number of copies sold as a function of S: Q(s) = ________
4. Assuming that the paper charges the profit-maximizing price, write an expression for profits as a function of Q and S. _____ Using the solution for Q(S) that you found in the last section, substitute Q(S) for Q to write an expression for profits as a function of S alone.__________
5. If the Daily Calumny charges its profit-maximizing price, and prints the profit-maximizing amount of scandal, how many column inches of scandal should it print? ______ How many copies are sold _____ and what is the amount of profit for the Daily Calumny if it maximizes its profits? _____