Question
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A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book
printed. The total production cost (in dollars) is given by the function , where is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function .
Let be the profit made (In dollars). Write an equation relating to N . Simplify your answer as much as possible.
P=

Ask by Black Horton. in the United States
Dec 08,2024

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Tutor-Verified Answer

Answer

P = 14.65N - 750

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The Deep Dive

First, let’s define the profit as the difference between total revenue and total production cost . Using the given equations, we have:
Substituting the expressions for and :
Now, simplify the equation:
So, the equation relating profit to the number of books is:

In the world of publishing, small presses often face the challenge of balancing costs and revenue. A key to success is understanding the break-even point, which is the number of books that need to be sold to cover costs. For this situation, you can find the break-even point by setting and solving for . This tells you how many copies need to fly off the shelves before profits start rolling in!
From an entrepreneurial angle, maximizing profit isn’t just about selling more books; it’s also about managing costs effectively. Consider strategies like negotiating better printing prices or improving marketing efforts to boost sales. Small changes can have a large impact on that profit margin. Plus, connecting with readers via social media or local events can foster a community around your book, leading to even more sales!

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