$4$Y$8.$ Ponchon$-$Savarit $($Prob$.13-2$ in Luyben, Chemical Process Analysis$)$ Using the enthalpy$-$composition diagram given in the diagram provided below for the methanol$-$water system, calculate the number of stages required and the feed plate location to produce $98$ weight percent methanol liquid product and $5$ percent methanol bottoms product from a feed of $45$ weight percent methanol entering the column at $50C.$ The column has a total condenser and a partial rehoiler, and operates at $1\mathrm{.}5$ times minimum reflux. What is the reboiler heat duty in Btu$/$hr if the feed rate is $5,000lb\frac{m}{h}r?$ What is the condenser duty?