Question
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=
printed. The total production cost
The total revenue earned (in dollars) from selling the books is given by the function
Let
P=
Ask by Black Horton. in the United States
Dec 08,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
P = 14.65N - 750
Solution

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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!