Hydrocarbon Distillation at $5$atm

A distillation column is separating ethane, propane, and $n-$butane at $5$atm. Operation is at total reflux. We want a $98\mathrm{.}9\%$ recovery of ethane in the distillate and a $99\mathrm{.}8\%$ recovery of n$-$butane in the bottoms. Propane is a sandwich component $($e$.$g$.,$ in between light and heavy keys$).F=100$kmo$\frac{l}{h}$ and is $30$mol$\%$ ethane, $33$ mol$\%$ propane and $37$mol$\%n-$butane. The feed is a saturated liquid.

Assume relative volatilities are constant, ${}_{EB}=13\mathrm{.}14,$ and ${}_{PB}=3\mathrm{.}91.$

a$)$ At total reflux find Nmin.

b$)$ At total reflux find the fractional recovery of propane in the distillate.

c$)$ At total reflux find distillate flow rate D$.$