$(30$ pts$)$ A mixture of $x(1),$ Y $(2),Z(3),$ and $W(4)$ is separated in a distillation column at $4\mathrm{.}9$ atm. The feed molar flow rate is $1000$kmo$\frac{l}{h}.$ Feed is composed of $8$mol$\%x,33$mol$\%Y,49$mol$\%Z,$ and $10$mol$\%W.$ The feed is saturated liquid. A $99\mathrm{.}7\%$ recovery of $Y$ is desired in the distillate. A $99\mathrm{.}8\%$ recovery of $Z$ is desired in the bottoms. There is no $x$ in the bottoms and no $W$ in the distillate. Find the minimum number of stages and minimum reflux ratio for the following relative volatilities. Take ${}_{4-3}=0\mathrm{.}29.$

$\backslash$table$[[$Student No$,{}_{1-3},{}_{2-3}$