Question 262178
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.