Methanol $($M$)$ is separated from ethanol $(E)$ by the distillation process shown the below figure. Assuming that

methanol and ethanol form an ideal solution and have a constant relative volatility $(a=1\mathrm{.}745).$

Determine:

$1\mathrm{.}1.$ The number of equilibrium stages.

$1\mathrm{.}2.$ Optimal location for the feed stage.

$1\mathrm{.}3.$ Optimal location for the liquid side stream.