The costs of the two methods will be equal when 4592 books are produced.
Define the cost equation
Let's say the number of books produced is x. We can represent the total cost for each method using the following equations:
Method 1: Total cost = Fixed cost + Variable cost per book * Number of books
Method 2: Total cost = Fixed cost + Variable cost per book * Number of books
Setting these two equations equal to each other since the total cost should be the same for both methods at the break-even point:
Fixed cost_1 + Variable cost_1 * x = Fixed cost_2 + Variable cost_2 * x
Substitute the given values
Now, we can substitute the given values for the fixed and variable costs of each method:
52939 + 10.75 * x = 17351 + 18.50 * x
Solve for x
To find the number of books (x) for which the costs are equal, we need to isolate x:
(18.50 - 10.75) * x = 52939 - 17351
7.75 * x = 35588
x = 35588 / 7.75
x ≈ 4592
Therefore, the publishing company needs to produce approximately 4592 books for the costs of the two methods to be the same.
Question:-
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such) as printing). There are two production methods it could use. With one method, the one-time fixed costs vilil total $52, 939, and the variable costs will be $10.75 per book. With the other method, the one-time fixed costs will total $17, 351, and the variable costs will be $18, 50 per book. For how many books produced will the costs from the two methods be the same?