A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $57,00, and variable costs (printing, paper, binding, shipping) at $2.90 for each book produced. If the book is sold to distributors for $11 each, how many must be produced and sold for the publisher to break even?
Let X be the number of books produced and sold for the publisher to break even.
The total cost (TC) for producing and selling X books is given by: TC = Fixed costs + Variable costs
The fixed costs are $57,000.
The variable costs are $2.90 per book, so the total variable cost for X books is 2.90X.
The total revenue (TR) from selling X books is given by: TR = Selling price per book * Number of books = $11X
To break even, the total cost should be equal to the total revenue: TC = TR
So, 57,000 + 2.90X = 11X
Combining like terms: 11X - 2.90X = 57,000
8.1X = 57,000
Dividing both sides by 8.1: X = 57,000 / 8.1
X ≈ 7,049
Therefore, approximately 7,049 books must be produced and sold for the publisher to break even.
To calculate the breakeven point in this scenario, we need to consider the fixed costs, variable costs, and the selling price per book.
Let's denote the number of books to be produced and sold as 'x'.
The fixed costs are given as $57,000.
The variable cost per book is $2.90.
The selling price per book is $11.
To break even, the total revenue from selling the books should cover both the fixed and variable costs.
The total revenue is the selling price multiplied by the number of books sold: 11x.
The total cost is the sum of fixed and variable costs: 57,000 + 2.90x.
Now we can set up the equation for the breakeven point:
11x = 57,000 + 2.90x
First, we subtract 2.90x from both sides:
11x - 2.90x = 57,000
Combine like terms:
8.1x = 57,000
Next, divide both sides by 8.1 to isolate x:
x = 57,000 / 8.1
Simplifying the expression:
x = 7,050
Therefore, the publisher must produce and sell 7,050 books to break even.