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 \( C=16.95 N+550 \), where \( N \) is the number of books. The total revenue earned (in dollars) from selling the books is given by the function \( R=31.90 N \). Let \( P \) be the profit made (in dollars). Write an equation relating \( P \) to \( N \). Simplify your answer as much as possible.

To determine the profit \( P \) in terms of the number of books \( N \), we start by using the given functions for total revenue \( R \) and total production cost \( C \): - **Revenue:** \( R = 31.90N \) - **Cost:** \( C = 16.95N + 550 \) Profit is calculated as the difference between revenue and cost: \[ P = R - C \] Substituting the given expressions: \[ P = 31.90N - (16.95N + 550) \] Simplify the equation by distributing the negative sign and combining like terms: \[ P = 31.90N - 16.95N - 550 \] \[ P = (31.90 - 16.95)N - 550 \] \[ P = 14.95N - 550 \] **Final Equation:** \[ P = 14.95\,N\ -\ 550 \]