Chapter 7.CR, Problem 93CR

Net Savings A company has installed new machinery that will produce a savings rate (in thousands of dollars per year) of

$S^{\prime }\left(t\right)=225-t^2$,

where $t$ is the number of years the machinery is to be used. The rate of additional costs (in thousands of dollars per year) to the company due to the new machinery is expected to be

$C^{\prime }\left(t\right)=t^2+25t+150$.

For how many years should the company use the new machinery? Find the net savings (in thousands of dollars) over this period.