You are given an ethanol$-$water mixture to treat in a distillation column to produce a distillate product at a rate of $150$kmo$\frac{l}{h}r$ at a mol fraction of $0\mathrm{.}95$ for ethanol. The bottoms product should not contain more than $0\mathrm{.}14$mol fraction ethanol. Calculate the flow rates of the feed stream and bottoms product stream if $54\%$ of the ethanol in the feed stream is recovered to the distillate stream. Determine the operating lines for the different sections. A side stream is extracted at a rate of $25\%$ of that of the feed rate and has a mol fraction of $0\mathrm{.}7$ of ethanol. A reflux ratio of $2\mathrm{.}5$ is applied.

$(15)$