A binary mixture is fed to a continuous fractionating column at bubble point, the feed rate is $100$ kmol$/$h$,$ the concentration of feed is $0\mathrm{.}4($mole fraction$),$ the concentration of distillate is $0\mathrm{.}9($mole fraction$),$ the concentration of liquid leaving the reboiler is $0\mathrm{.}1($mole fraction$),$ and the reflux ratio is $3.$ The vapor from the top plate are totally condensed but not cooled. The relative volatility is $2\mathrm{.}45.$ Calculate:$($a$)$ The flow rate D kmol$/$h of overhead product and B kmol$/$h of bottom product.$($b$)$ Minimum reflux.$($c$)$ The flow rate of vapor from the reboiler V$\text{'}$ kmol$/$h$.($d$)$ The operating line equation of Rectifing section and Stripping section$($e$)$ The concentration of liquid leaving the ideal plate above the reboiler Xn$.$