$(50$ points$)$ A mixture of compounds A and $B$ are being separated using the combined extraction

and distillation system depicted below.

$100mo\frac{l}{h}r$ of the A and B mixture enters in stream $1$ with a mol fraction of A of $0\mathrm{.}824$

Pure C enters in stream $2$ and combines with a recycle stream before entering the extractor

$($stream $3)$

All of the A exits the extractor in stream $4.$

$99\mathrm{.}0\%$ of the $C$ in stream $3$ exits the extractor in stream $5.$

$80\mathrm{.}0\%$ of the B in stream $5$ exits the distillation column in stream $6.$

a$)$ Redraw the flow chart in and label it using component molar flow rates instead of overall molar

flow rates and mol fractions. $(10$ points$)$

b$)$ Write out the $11$ equations needed to solve the problem in linear form. $(10$ points$)$

c$)$ Put the $11$ equations in matrix form $.(10$ points$)$

d$)$ Solve the matrix equation by inverting the A matrix using Excel, Python, or another method of

your choosing $($make sure to show screenshots of all your work$).(10$ points$)$

e$)$ Convert your component flow rates back into total molar flow rates and mole fractions and fill in

all the unknown values in the flow chart shown above. $(10$ points$)$send expert