More specifically, $10$ wt$.\%$ ethanol will be bought as the raw materials and $80$ wt$.\%$ of ethanol will

be sold as product to downstream processing factory. You do not need to work on the membrane

part. The distillation column will have $98\%$ ethanol recovered from the top. Assume $100,000$

tons$/$year of $80$ wt$.\%$ of ethanol will be produced. The price of the $10$ wt$.\%$ ethanol is purchased

at a price of $$25/$ton$,$ and the $80$ wt$.\%$ ethanol is sold at $$350/$ton $($the product price fluctuation on

economic viability should also be considered at the end$).$ Maximum of $3$ students per project and

the contribution of each student has to clearly stated or points will be deducted for all students.

You need to finish following tasks for the project.

$1.$ Use CMO assumption, manually find the number of stages and optimum feed location:

$$ Find the minimum reflux ratio and use that to choose your reflux ratio.

$$ Find the number of stages and optimum feed location with the McCabe$-$Thiele method.

$$ Determine the column efficiency and find real column stage number and feed location. give me proper calculation for distillation