Break-even point of a small business

Statement

The Zanni firm makes notebooks with total cost $C(q)=200+3q$ (in €) and sells them at $5\ \text{€}$ each, with revenue $R(q)=5q$. How many notebooks must it sell to reach the break-even point (revenue $=$ cost)?

Solution

At break-even $R(q)=C(q)$: $5q=200+3q\iff 2q=200\iff q=\boxed{100\ \text{notebooks}}.$ (Below $100$ units the firm makes a loss, above it makes a profit.)