A trayed tower is to be designed to continuously distill $450$ Kmol$/$hr of a binary mixture of $60$ mol$\%$ benzene and $40$ mol$\%$ toluene. A liquid distillate and bottom product of $95$ mol$\%$ and $5$ mol$\%$ benzene is to be produced. The feed is a two$-$phase mixture consisting of $50$ mole$\%$ liquid. Use the McCabe$-$Thiele method to compute the following, assuming a uniform pressure of $1$ atm throughout the column. Use the equilibrium data graph attached to determine;

a$)$ The flow of the distillate and bottom $(10$ marks$)$

b$)$ The minimum number of stage $($Nmin$)(6$ marks$)$

c$)$ The number of theoretical trays needed if the reflux ratio is $1\mathrm{.}3$ Rm $(12$ marks$)$

d$)$ The entering stage of the feed entering