Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university

and to local businesses and residences in the Blacksburg area. The plant burns three types of coal which produce steam

that drives the turbines that generate the electricity. The Environmental Protection Agency $($EPA$)$ requires that for each ton of

coal burned, the emissions from the coal furnace smoke stacks contain no more than $2,500$ parts per million $($ppm$)$ of sulfur

and no more than $2\mathrm{.}8$ kilograms $($kg$)$ of coal dust.