Chapter 2.4, Problem 115E

Business: total cost. Certain costs in business can be separated into two components: those that increase with volume and those that decrease with volume. For example, customer service becomes more expensive as its quality increases, but part of the increased cost is offset by fewer customer complaints.

Katie’s Clocks determines that its cost of service, $C\left(x\right)$, in thousands of dollars, is modeled by

$C\left(x\right)=\left(2x+4\right)+\left(\frac{2}{x-6}\right),x>6,$

where x represents the number of “quality units.” Find the number of “quality units” that the firm should use in order to minimize its total cost of service.