$2-$Feed containing $60\%$ benzene, $30\%$ toluene and $10\%$ xylene is purified by a distillation system. The product at the top of the tower must contain at least $90\%$ benzene and the amount of xylene can be omitted. The product at the bottom of the tower should not contain more than $60\%$ toluene. The feed enters the tower at the boiling point and is R$4.$ It is desirable to determine the number of required trays and the approximate location of feed entry. The relative volatility coefficient of benzene to toluene is equal to $4\mathrm{.}2$ and the relative volatility coefficient of xylene to toluene is equal to $45\mathrm{.}0$ and it can be assumed that the volatility coefficients remain constant throughout the tower.