Question

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?

Answer 1

To find the price that gives you the maximum revenue, you need to determine the demand curve based on the given information and then calculate the revenue equation. By differentiating the revenue equation, you can find the price that maximizes the revenue.

Step-by-step explanation:

To find the price that gives you the maximum revenue, you need to determine the demand curve based on the given information. Since the demand for books depends linearly on the price, we can assume that the demand curve follows the equation Q = a - bP, where Q is the quantity sold and P is the price. Using the given data, we can calculate the values of a and b.

Using the first week of classes data, Q1 = 140 and P1 = $10. Plugging these values into the demand equation, we get 140 = a - 10b. From the second semester data, Q2 = 0 and P2 = $30. Plugging these values into the demand equation, we get 0 = a - 30b.

Solving these two equations simultaneously, we can find the values of a and b. Once we have the demand curve equation, we can calculate the revenue equation, R = P * Q, and differentiate it with respect to P to find the maximum revenue.

Answer 2

I think 10 sorry if I am incorrect. Good luck!