Q$14.$ A mixture of $4\%$ n$-$pentane, $40\%$ n$-$hexane, $50\%$ n$-$heptane and $6\%$ n$-$octane is distilled at $1$atm. The goal is to recover $98\%$ of $n-$hexane and $1\%$ of $n-$heptane in the distillate. The feed is boiling liquid. $($i$)$ Find minimum number of stages and minimum reflux ratio. $($ii$)$ Given operating reflux of $1\mathrm{.}5$ of the minimum, find the operating number of ideal stages. The $K_i$ values of n$-$pentane, n$-$hexane, n$-$heptane and n$-$octane are $3\mathrm{.}62,1\mathrm{.}39,0\mathrm{.}56$ and $0\mathrm{.}23$ respectively.