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 ( c = 750+15.95n ), where ( n ) is the number of books. the total revenue earned (in dollars) from selling the books is given by ( 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.

Explanation:

Step1: Recall Profit Formula

Profit \( P \) is revenue \( R \) minus cost \( C \), so \( P = R - C \).

Step2: Substitute R and C

Given \( R = 31.90N \) and \( C = 750 + 15.95N \), substitute into the profit formula:
\( P = 31.90N - (750 + 15.95N) \)

Step3: Simplify the Expression

Distribute the negative sign: \( P = 31.90N - 750 - 15.95N \).
Combine like terms (\( 31.90N - 15.95N \)): \( 31.90 - 15.95 = 15.95 \), so \( P = 15.95N - 750 \).

Answer:

\( P = 15.95N - 750 \)