Question $1$: Cost Analysis $(25\%)$

Assume you were recently hired as the director of the Solid Waste Department for Murky County. Your department operates both a solid waste collection system $($a fleet of garbage trucks$),$ and a landfill where garbage is disposed. Only garbage from the county is disposed at the landfill, and all county garbage is now collected by your department.

Your budget has been funded by user charges paid by residents of the county based on the volume of garbage. The charge is $$1\mathrm{.}3$ per bag of garbage collected. The county provides the bags free of charge to residents and only garbage in these bags is collected. $($You can assume that garbage collection for business is handled separately.$)$ Unfortunately, recent increases in the cost of fuel, salaries, and chemicals have led to deficits in the "Solid Waste Fund" and have had to be subsidized by county property taxes. The County Administrator is looking for recommendations on how this deficit can be eliminated.

Before undertaking this analysis, you have collected the following information on the present operation:

Overhead costs: $$500,000$