Question 1203526: 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 . The variable costs will be per book. The publisher will sell the finished product to bookstores at a price of per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52803)   (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 . The variable costs will be per book. The publisher
will sell the finished product to bookstores at a price of per book. How many books
must the publisher produce and sell so that the production costs will equal the money from sales
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! let x equal the number of books produced and sold.
let c = total cost
let f = fixed cost
let v = vriable cost
let s = sale price per book.
let r = total revenue
let p = total profit.
your equations are:
c = f + x * v
r = x * s
p = r - c
you break even when p = 0
when p = 0, you get 0 = r - c
add c to both sides of the equaiton and you get c = r
switch sides and you get r = c.
assuming r = c, then:
replace r with x * s and replace c with f + x * v
you get x * s = f + x * v
subtract x * v from both sides of the equation to get:
x * s - x * v = f
that's your break even equation.
when that occurs, your revenue from sales will equal your total production costs.
as an example:
asume f = 5000 and v = 2.5 amd s = 3
break even is when r = c
that becomes when x * s = f + x * v
since f = 5000 and v = 2.5 and s = 3, the equation becomes:
x * 3 = 5000 + x * 2.5
subtract x * 2.5 from both sides of the equation to get x * 3 - x * 2.5 = 5000
simplify to get .5 * x = 5000
solve for x to get x = 5000 / .5 = 10,000
you will break even when you produce and sell 10,000 books.
your revenue will be 10,000 * 3 = 30,000
your production cost will be 5000 + 2.5 * 10,000 = 5000 = 25,000 = 30,000
total sales = total cost = break even.
your profit will be 0 at break even point.
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