$(25$ points$)$ A distillation column with a total condenser and partial reboiler is separating acetone $($the more volatile component$)$ from ethanol at $1$ atmosphere. As pictured, there are two feeds with flow rates $F1=100mo\frac{l}{h}r$ and $F2=200mo\frac{l}{h}r.$ Feed $1$ has $F1=0\mathrm{.}7$ and is a saturated liquid. Feed $2$ has $xF2=0\mathrm{.}4$ and is a superheated vapor where approximately $1$ mole of liquid will vaporize on the feed stage for each $10$ moles of feed. We desire $xD=0\mathrm{.}95$ and $xw=0\mathrm{.}05.R=2^{**}$Rmin. Use Feed $1$ to determine Rmin. Constant molar overflow $($CMO$)$ is valid. How many stages are needed to achieve this separation and what is the optimal feed stage for Feed $1?$