Let's consider a system consisting of two distillation columns, where the first column the bottom product stream is fed to the second column. $30000$ kg$/$ of mixture enters the first column, the mixture

contains $50\%$ benzene, $30\%$ toluene and $20\%$ xylene. The distillate in the first column contains $95\%$ benzene, $3\%$ toluene and $2\%$ xylene. The distillate from the second column contains $3\%$ benzene, $95\%$ toluene and $2\%$ xylene. Furthermore, it is known that $52\%$ of the total mass fed to the first column ends up into the distillate of the first column and that $75\%$ of the benzene fed into the second column ends up in the second column

to the distillate. All concentrations are given as mass percentages.

Use degrees of freedom analysis to see if it is possible

a$)$ solve the column balances one by one.

b$)$ solve the column balances together.

c$)$ solve the balance of the overall process.