Question 1002429: Please help me solve this question thanks in advance.
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). The one-time fixed costs will total $41,874. The variable costs will be $8.75per book. The publisher will sell the finished product to bookstores at a price of $19.25per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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).
The one-time fixed costs will total $41,874.
The variable costs will be $8.75per book.
The publisher will sell the finished product to bookstores at a price of $19.25per book.
How many books must the publisher produce and sell so that the production costs will equal the money from sales?
This is called the "break-even" point
:
let x = no. of books printed
the cost equation
C(x) = 8.75x + 41874
The revenue equation, (amt received by retail sales)
R(x) = 19.75x
Break-even point occurs when revenue equals cost: R(x) = C(x)
19.75x = 8.75x + 41874
19.75x - 8.75x = 41874
11x = 41874
x = 41874/11
x = 3806.7, you break even when you sell the 3,807th bood
:
:
Prove this to yourself find the actual cost and revenue
C(x) = 8.75(3807) + 41874)
C(x) = 33311.25 + 41874
C(x) = $75185.25
Revenue total
R(x) = 19.75(3807)
R(x) = 75188.25, a slight profit when you sell the 3807th book
:
When you sell the 3806th book: 75168.50, a 16.75 loss
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