Question

A company has installed new machinery that will produce a savings rate (in thousands of dollars per year) of S'(x) = 225-x^2, where x is the number of years the machinery is to be use. The rate of additional costs (in thousands of dollars per year) is expected to be C'(x) = x^2-25x+150. For how many years should the company use the new machinery? Find the net savings (in thousands of dollars) over this period.

Answer 1

After 15 years the use of said machine is no longer profitable

Explanation:

it should be used, as long as the money generated is not smaller as the costs generated. By setting both formulas equal (calculating the x value for when they are equal) you get x = 15 and x = -2.5(which doesnt make sense in this context).