The mixture containing $40\%$ Benzene by Weight $-60\%$ Toluene shall be distilled in a continuously operating distillation column with the upper product $(\frac{n}{n})97\%$ benzene and the lower product $(\frac{n}{n})98\%$ toluene. The speed of the feed current is $13000k\frac{g}{h},$ the backflow rate is $3\mathrm{.}5$:$1$mol top product. for the case when $\frac{2}{3}$ of the feed is liquid and $\frac{1}{3}$ is steam,

a$)$ Calculate the minimum yield rate

b$)$ determine the ideal number of stages and from which stage the feeding is made.

$\backslash$table$[[x,0\mathrm{.}02,0\mathrm{.}04,0\mathrm{.}05,0\mathrm{.}07,0\mathrm{.}09,0\mathrm{.}09,0\mathrm{.}14,0\mathrm{.}21,0\mathrm{.}43,0\mathrm{.}60,0\mathrm{.}78,0\mathrm{.}85,0\mathrm{.}93,0\mathrm{.}99],[y,0\mathrm{.}04,0\mathrm{.}09,0\mathrm{.}14,0\mathrm{.}21,0\mathrm{.}22,0\mathrm{.}24,0\mathrm{.}32,045,0\mathrm{.}68,0\mathrm{.}80,0\mathrm{.}91,0\mathrm{.}95,0\mathrm{.}97,0\mathrm{.}99]]$