The profit function is given by $P(x) = 18x - 360$. We need to find the break-even quantity, which means finding the value of $x$ when the profit $P(x)$ is equal to 0.

1. Problem Description

The profit function is given by $P(x) = 18x - 360$. We need to find the break-even quantity, which means finding the value of $x$ when the profit $P(x)$ is equal to

0.

2. Solution Steps

To find the break-even quantity, we set the profit function $P(x)$ equal to 0 and solve for $x$:

$P(x) = 0$

$18x - 360 = 0$

Add 360 to both sides of the equation:

$18x = 360$

Divide both sides by 18:

$x = \frac{360}{18}$

$x = 20$

3. Final Answer

The break-even quantity is $x = 20$ units.