A distillation column is separating $2-$Methyltetrahydrofuran from Cumene. The column has a partial reboiler, a total condenser and a saturated liquid reflux. Feed rate it $100$ kmol$\frac{e}{h}r$ and feed composition is $50$ mole$\%2-$Methyltetrahydrofuran. Feed is a superheated vapor. $1$ mole of liquid will vaporize to cool $5$ moles of feed to dew point. Bottom product that is $98$ mole$\%$ Cumene and distillate product that is $96$ mole$\%2$Methyltetrahydrofuran are desired. Constant molal overflow is assumed.

i$)$ Plot the feed line in the McCabe Thiele diagram provided.

ii$)$ Calculate the minimum reflux ratio.

iii$)$ For an actual reflux ratio of $R=2R_{\text{m}\text{i}\text{n}},$ find the total number of stages needed for the separation if the feed stage is the first stage above the reboiler. Begin counting stages from the bottom up$.$

Hints: Use McCabe diagram provided.