To calculate C(x), the publisher's costs as a function of x, we add the fixed cost of $12,400 to the cost per book of $5.75 times the number of books produced:
C(x) = $12,400 + $5.75x
To calculate R(x), the publisher's revenue as a function of x, we multiply the revenue per book of $7.75 by the number of books sold:
R(x) = $7.75x
To find the number of books the publisher must produce and sell to break even, we set the cost function equal to the revenue function:
$12,400 + $5.75x = $7.75x
Solving for x:
$12,400 = $2x
x = $12,400 / $2
x = 6200 books
Therefore, the publisher must produce and sell 6200 books to break even.
Their costs to produce 6200 books would be:
C(6200) = $12,400 + $5.75(6200) = $12,400 + $35,650 = $48,050
Their revenue from selling 6200 books would be:
R(6200) = $7.75(6200) = $48,050
So, the publisher's costs to produce 6200 books would be $48,050 and their revenue from selling 6200 books would also be $48,050.
When a company produces a product, the amount that they must pay in order to produce the product is referred to as their costs. Some costs are fixed, that is, the company must pay the same amount, no matter how many products they make. Other costs vary depending on how many products they make. A company's income is referred to as its revenue. One way that companies make revenue is by selling products at a set price.
To release a new book, a publisher has fixed costs of $12,400 and a cost per book of $5.75. When the book is sold, the publisher receives revenue of $7.75 per book.
Write an expression to give the publisher's costs as a function of x, the number of books they produce.
C(x)
Write an expression to give the publisher's revenue as a function of æ, the number of books they sell.
R(x)
A company is said to break even when its costs and revenue are equal. Using the functions you wrote above, and assuming that they sell all of the books they produce, find the number of books the publisher must produce and sell to break even. If necessary, round your answer to the nearest whole book.
books
What will their costs be to produce this number of books?
$
What will their revenue be when they sell this number of books?
$
1 answer
1 answer