A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed

Question

A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed. The total production cost C (in dollars) is given by the function C = 550 + 18.95N, where N is the number of books. The total revenue earned (in dollars) from selling the books is given by the function R = 31.90N. Let P be the profit made (in dollars). Write an equation relating P to N . Simplify your answer as much as possible.

Answer 1

First, we must recall an equation that related profit, revenue, and costs:

Profit = Revenue - Costs

P = R - C

To begin, substitute the expressions from each letter into the above equation:

P = (31.90N) - (550 + 18.95N)

The equation is now relating P to N. The next step is to simplify it:

P = (31.90N) - (550 + 18.95N)

Distribute the minus sign through the brackets:

P = 31.90N - 550 - 18.95N

Combine like terms:

P = 12.95N - 550

It is now fully simplified.