Question

A small publishing company is releasing a new book. The production costs will include a onetime fixed cost for editing and an additional cost for each printed. The total production cost C (in dollars) is given by the function C = 550 + 19.95N , where N is the number of books The total revenue earned (in dollars) from selling the books is given by the function R = 32.80N Let P be the profit made in dollars). Write an equation relating P to N. Simplify your answer as much as possible P =

Answer 1

We have a cost function C(N) and a revenu function R(N) defined as:

`\begin{gathered} C(N)=550+19.95N \\ R(N)=32.80N \end{gathered}`

The profit is defined as the difference between the revenue and the cost, so we can define a profit function as:

`P(N)=R(N)-C(N)`

We can replace with the definition of each function and rearrange as:

`\begin{gathered} P(N)=R(N)-C(N) \\ P(N)=32.80N-(550+19.95N) \\ P(N)=(32.80-19.95)N-550 \\ P(N)=12.85N-550 \end{gathered}`

Answer: the profit function is P = 12.85N - 550.