SOLUTION: I have this multi-level equation i have to create with this information: A publishing company will publish an authors book. Estimated cost is $75,000 + $5.50 per book printed

Question 262178: I have this multi-level equation i have to create with this information:
A publishing company will publish an authors book.
Estimated cost is $75,000 + $5.50 per book printed
Selling price is $15 per copy.
Publisher will retain 40 percent of the selling price as a commission, let X represent the number of copies printed and sold.
a) Find the Cost Function: C(x);
b) Find the Revenue Function: R(x);
c) Find the Profit Function: P(x);
d) How many copies must be sold to break even?
e) whats the profit of the company if 46,000 copies are sold?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
from the standpoint of the publishing company, this is what is happening as far as I can make out from the problem statements.

equation for cost function is:

c(x) = 75,000 + 5.50 * x

this is the cost to the publishing company that covers the cost of printing the books.

equation for revenue function is:

r(x) = .4 * 15 * x

this is the revenue to the publishing company. it is assumed some other company such as the retailer is selling the book. the retailer keeps 60% and the publisher gets 40% of the sale price.

equation for profit function is:

p(x) = r(x) - c(x)

this is the profit to the publisher. publisher pays for costs of printing the books and gets revenue from the retailer when the retailer sells the book. the difference between the cost to the publisher and the revenue to the publisher is the profit to the publisher.

publisher will break even when r(x) = c(x). at that point, there will be no profit.

our equations are:

c(x) = 75,000 + 5.50 * x
r(x) = .4 * 15 * x

break even point is when r(x) = c(x) which becomes:

75,000 + 5.50 * x = .4 * 15 * x

simplify this equation to get:

75,000 + 5.5*x = 6*x

subtract 5.5*x from both sides of this equation to get:

75,000 = .5*x

divide both sides of this equation by .5 to get:

x = 150,000

publisher will break even when 150,000 books are sold.

at that point, the cost to the publisher will be:

75,000 + 5.5 * 150,000 = 900,000

at that point the revenue to the publisher will be

.4 * 15 * 150,000 = 900,000.

revenue equals cost is the break even point.

if 46,000 copies are sold, then:

c(x) = 75,000 + 5.5*46,000 = 328,000.

r(x) = .4 * 15 * 46,000 = 276,000.

the publisher will have a loss of 328,000 - 276,000 = 52,000 dollars.

this stands to reason, since based on the assumptions, the publisher will not break even until 150,000 books qre sold.

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