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 $c = 19.95n+650$, 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.

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 \( C = 19.95N + 650 \), substitute into the profit formula:
\( P = 31.90N - (19.95N + 650) \)

Step3: Simplify the equation

Distribute the negative sign: \( P = 31.90N - 19.95N - 650 \)
Combine like terms: \( 31.90N - 19.95N = 11.95N \), so \( P = 11.95N - 650 \)

Answer:

\( 11.95N - 650 \)