An aqueous solution containing $40$ mol$\%$ Methanol is to be separated at a rate of $300$ kmol$/$h using open steam as the source of heat energy. The top product must have $96$ mol$\%$ Methanol and the bottom product must not have more than $4$ mol$\%$ Methanol in it$.$ The feed enters the column $50\%$ vaporized. A reflux ratio of $2\mathrm{.}25$ is suitable. The equilibrium data for Methanol$-$Water system at $101\mathrm{.}3$ kPa are given below: $0\mathrm{.}10\mathrm{.}30\mathrm{.}020\mathrm{.}130\mathrm{.}040\mathrm{.}230\mathrm{.}060\mathrm{.}30\mathrm{.}080\mathrm{.}370\mathrm{.}20\mathrm{.}5800\mathrm{.}670\mathrm{.}730\mathrm{.}780\mathrm{.}820\mathrm{.}870\mathrm{.}920\mathrm{.}960\mathrm{.}98$ Determine $($a$)$ The number of theoretical stages required for this separation $($b$)$ Location of feed plate $($c$)$ The equation of the stripping section operating line $($d$)$ the steam rate $($e$)$ the condenser heat load.