The feed $(245$kmo$\frac{l}{h}r)$consists of methonol and water containing $48$mole$\%$ methanol and $52$ mole $\%$ water. The averhead product is to contain $93$ mole $\%$ methal and the bottom product contains $4$ mole $\%$ methonol. The feed is cold and for each mole of feed, $0\mathrm{.}22$ moles of vapor is condensed on the feed plate. The colum runs with $R=1,85.$ Rmin, Assume constant relative volatility $a_{AB}=2\mathrm{.}8$

a$)$ Calculate the amount of distillate

b$)$ Calculate the bottom flow rate

c$)$ Calculate the bottom product flow rate

d$)$ Calculate $q$

e$)$ Calculate R

f$)$ Calculate the percent recovery of methond

g$)$ Calculate the slope of enriching section operating line.

h$)$ Calculate the slope of stripping section operating line.

$)$ Calculate the number of thearitical stages.

Please solve the step by step and explain with detail.