A distillation column with a total condenser and a partial reboiler is separating $200$mole$\frac{s}{h}$ of a feed that is $60$ mole $\%$ Toluene and $40$ mole $\%$ Benzene. The feed enters the column as a two$-$ phase mixture that is $30\%$ vapor. A distillate composition of $90$ mole $\%$ Benzene and a bottoms of $5\mathrm{.}0$mole$\%$ Benzene are desired. The reflux is returned as a saturated liquid, and CMO can be assumed. An external reflux ratio of R$/$D $=2\mathrm{.}6$ is used. Pressure $=101\mathrm{.}3$kPa. You can assume the relative volatility of Benzene to Toluene is $2\mathrm{.}5$

a$)$ Use the Lewis method to find the optimum feed location and the number of equilibrium stages needed to achieve the desired separation

b$)$ If the sixth internal stage above the reboiler is used as the feed stage, how many equilibrium

stages are needed for the separation?