$\"\"$

The total cost of operating a factory is $\"\"$ .

The avearage cost per unit is $\"\"$

Apply derivative with respect to $\"\"$ .

$\"\"$

Find the relative extremas by equating the first derivative to zero.

$\"\"$

So the factory have minimum average cost at $\"\"$ units.

$\"\"$

The factory have minimum average cost at $\"\"$ units.