Chapter 13.2, Problem 41E

(a)

To determine

To calculate: The function for the cost if Rate of change in cost in thousands of dollars per year of a new production line is

$C\text{'}\left(x\right)=\frac{60x}{5x^2+1}$

where $x$ is the number of years and fixed cost is $\$10\text{ thousand}$.

(b)

To determine

To calculate: Whether company should add new line after 5 years if New production line will be added if total cost of line for first 5 years remains below $\$40,000$.

The total cost function is

$C=6\cdot \ln \left(5x^2+1\right)+10$