Question

The demand for the book is given by p = 96 - 3q. A bookstore can order copies that will cost $1. If the bookstore orders 11 books, what is the total profit? Enter as a value.

Answer 1

The total profit is $594.

Step-by-step explanation:

To find the total profit, we first need to calculate the revenue and the cost. The revenue is the price per book multiplied by the quantity sold, which is given by:

R = p * q = (96 - 3q) * q = 96q - 3q^2

The cost is the cost per book multiplied by the quantity ordered. Since the cost per book is $1 and the quantity ordered is 11, the cost is:

C = $1 * 11 = $11

The profit is then calculated by subtracting the cost from the revenue:

Profit = R - C = (96q - 3q^2) - $11

Substituting q = 11 into the equation, we get:

Profit = (96 * 11 - 3 * 11^2) - $11 = $968 - $363 - $11 = $594.