Problem 2. A government agency is tasked with eliminating waste in their budget, that is,
money they simply should not be spending. In order to find and eliminate such spending
waste, the agency forms a division to locate overpayments, mismanaged accounts, etc., and
they find that last year they wasted $40,000,000 (of a very large budget), but they also find
that the cost to the agency, in millions of dollars, to eliminate $x$ percent of this wasteful
spending is
$C(x) = \frac{3x}{100 - x}$
i. How much money will it cost the agency to eliminate $8,000,000 in wasteful spending?
$30,000,000?
ii. What is $\lim_{x \to 100^{-}} C(x)$, and what is this telling us?
iii. Find $C'(x)$ and explain its meaning in words. What are the units of $C'(x)$?
iv. Is there a point at which it is no longer worth it for the agency to eliminate waste? If
so, what is that amount of waste, in dollars, and it not, then explain why not.
(Hint: Find a function of $x$ that tells you the net amount the agency saves, that is, the
amount they save while also taking into account the cost to save that amount.)