Your underground used-book business is booming. Your policy is to sell all used versions of Calculus and You at the same price (regardless of condition). When you set the price at $10, sales amounted to 140 volumes during the first week of classes. The following semester, you set the price at $30 and sales dropped to zero. Assuming that the demand for books depends linearly on the price, what price gives you the maximum revenue?

You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $75.00, two for $73.00 each, and in general the group rate per room is found by taking $2 off the base of $75 for each extra room rented. (b) Use a formula to give the rate you charge for each room if you rent n rooms to an organization. (c) Find a formula for a function R = R(n) that gives the total revenue from renting n rooms to a convention host. (d) Use functional notation to show the total revenue from renting a block of 7 rooms to a group. Calculate the value.

As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table. Price per Pound, p $3.00 $4.00 $5.00 Monthly Sales, q (pounds) 404 286 224 Ae-DP, where A and b are constants you must determine. (a) Use the sales figures for the prices $4 and $5 per pound to construct a demand function of the form q (Round A and b to two significant digits.) q = (b) Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.) p = $3 E = p = $4 E = p = $5 E = (c) At what price should you sell the cheese to maximize monthly revenue? (Round your answer to the nearest cent.) $ (d) If your total inventory of cheese amounts to only 200 pounds and it will spoil one month from now, how should you price it to receive the…