From a reactor in the methanol industry, a vapor$-$phase solution is produced at its dew point temperature, with a flow rate of $100$ kgmo$\frac{l}{h}$ containing $30$mol$\%$ methanol and the remainder being water. To increase the methanol concentration to $53$mol$\%$ to meet market demand, a multistage distillation process is used with a partial condenser operating at a pressure of I atm with a reflux ratio of $1\mathrm{.}5$ times the minimum reflux. To ensure that the bottom product of the distillation column can be directly processed in the waste treatment unit, the methanol concentration must be less than $5$mol$\%.$ Determine the number of ideal stages required and the feed tray number using the McCabe$-$Thiele method.

Methanol mole fraction in vapor$-$liquid equilibrium:

$\backslash$table$[[x,0,0,1,0,3,0,5,0,7,1,0],[Y,0,0,3,0,6,0,8,0,9,1,0]]$