Final answer:
The bookstore will make a total profit of $576 by selling 9 books, calculated by subtracting the total cost from the total revenue obtained from selling the books at the price determined by the demand equation.
Step-by-step explanation:
The demand for the book is given by the equation P = 96 – 3Q, where P is the price at which the books are sold and Q is the quantity of books sold. The cost per book for the bookstore is $5. If the bookstore orders 9 books, we can calculate the total revenue and then the total profit.
First, we'll find the selling price for 9 books. Substituting Q with 9 into the demand equation:
P = 96 – 3(9)
P = 96 – 27
P = $69
So, each book is sold for $69 when 9 books are sold. To calculate the total revenue for 9 books:
Total Revenue = Price × Quantity
Total Revenue = $69 × 9
Total Revenue = $621
Next, we calculate the total cost for the bookstore to purchase the 9 books:
Total Cost = Cost per book × Quantity
Total Cost = $5 × 9
Total Cost = $45
Finally, we calculate the total profit which is total revenue minus total cost:
Total Profit = Total Revenue – Total Cost
Total Profit = $621 – $45
Total Profit = $576