Question $1.(40$ marks$)$

Regulatory agencies and others generally estimate the amount of municipal solid waste generated per person per day to be $5$ pounds. The U$.$S$.$ Environmental Protection Agency and others have made a few measurements of the composition of solid waste. The information tabulated below is a typical estimate of the composition of municipal solid waste in the United States.

$\backslash$table$[[$Description$,\backslash$table$[[$Percentage by$],[$weight$]],\backslash$table$[[$Unit weight$],[($pcf$)]]],[$Paper products,$10\mathrm{.}0,5\mathrm{.}1],[$Corrugated cardboard,$30\mathrm{.}6,3\mathrm{.}6],[$Aluminum$,1\mathrm{.}5,5\mathrm{.}0],[$Glass$,8\mathrm{.}0,12\mathrm{.}1],[$Ferrous metals,$7\mathrm{.}1,20\mathrm{.}0],[$Plastics$,7\mathrm{.}1,4\mathrm{.}0],[$Food waste,$7\mathrm{.}8,18\mathrm{.}0],[$Yard waste,$18\mathrm{.}1,6\mathrm{.}5],[$Other$,9\mathrm{.}8,30\mathrm{.}0],[$Total$,100\mathrm{.}0,]]$

Compute the following using the tabulated data:

$1$ a$)$ The weight of $1$ cubic yard of solid waste.

$1$ b$)$ The percentage reduction in weight and volume, if $50\%$ and $100\%,$ respectively, of the following component is removed from the waste stream.

a$.$ Paper products and corrugated cardboard

b$.$ Aluminum

c$.$ Glass

d$.$ Ferrous metals

e$.$ Food wastes

f$.$ Yard wastes

$1$ c$)$ Food wastes and yard wastes could be removed from the waste stream and composted. What is the expected percentage reduction in weight and volume if $50\%$ and $100\%$ respectively, of these materials are removed from the waste stream.

Note: $1$ cubic yard $=27$ cubic feet.