$3\mathrm{.}8$ A $1,000$ MW coal$-$fired power plant operates at $40\%$ efficiency. It consumes $10,000$ tons of coal$/$day$.$ The plant uses coal that is $4\%$ sulfur and $10\%$ ash. The ash leaves the furnace as bottom ash or fly ash. Virtually all the sulfur is converted to sulfur dioxide, and the plant is equipped with a $90\%$ efficient $S{O}_2$ scrubber. Assume that one$-$third of the ash in the coal forms bottom ash, and the remainder forms fly ash. Pollution control devices capture $98\%$ of the fly ash. Calculate the rates $($each in tons$/$day$)$ of:

a$.$ sulfur dioxide emissions

b$.$ bottom ash removed from the furnace

c$.$ fly ash collected

d$.$ emissions of fly ash to the atmosphere