In the production of soybean oil, dried and flaked soybeans are brought into contact with a solvent $($often hexane$)$ that extracts the oil and leaves behind the residual solids and a small amount of oil. The soybeans contain $18\mathrm{.}5wt\%$ oil and the remainder insoluble solids, and the hexane is fed at a rate corresponding to $2\mathrm{.}0kg$ hexane per $kg$ beans. The residual solids leaving the extraction unit contain $35\mathrm{.}0wt\%$ hexane, all of the non$-$oil solids that entered with the beans, and $1\mathrm{.}0\%$ of the oil that entered with the beans. $1000k\frac{g}{h}$ of dried flaked soybeans are fed to the process unit.

a$.$ Draw a flowchart of the process, labeling the two feed streams $($beans and solvent$)$ and the leaving streams $($solids and extract$)$ with standard variables to denote amount and composition for each stream.

b$.$ Carry out a degrees of freedom analysis. Write out the system of independent mass balances in terms of the symbols on your flowchart. Write out the "other equations" that will be used to specify the process.

c$.$ Calculate the mass flow rates of the extract and residual solids, and the composition of the extract.