A trayed tower operating at $1$ atm is to be designed to continuously distill $200$ kmol$/$h $(55\mathrm{.}6$ mol$/$s$)$ of a binary mixture of $60$ mol$\%$ benzene, $40$ mol$\%$ toluene. A liquid distillate and a liquid bottoms product of $95$ mol$\%$ and $5$ mol$\%$ benzene, respectively, are to be produced. Before entering the column, the feed$-$originally at $298$ K$-$is flash$-$vaporized at $1$ atm to produce an equimolal vapor$/$liquid mixture $($Vf$/$F$=$Lf$/$F$=0\mathrm{.}5).$ A reflux ratio $30\%$ above the minimum is specified. Calculate:

$($a$)$ The quantity of the products.

$($b$)$ The minimum number of theoretical stages

$($c$)$ The minimum reflux ratio.

$($d$)$ The number of equilibrium stages and the optimal location of the feed stage for the reflux ratio specified.

$($e$)$ The thermal load of the reboiler