A clarified cultivation homogenate has following components before ultrafiltration: $1$ mg$/$L of recombinant protein, $25$ mg$/$L of polysaccharide and $2$ g$/$L of glucose. The retention coefficients of the ultrafiltration membrane are: $0\mathrm{.}95$ for recombinant protein, $0\mathrm{.}69$ for polysaccharide and $0$ for glucose. Finally, polysaccharide retentate concentration is $142$ mg$/$L$.$

Q$1$:a$)$ What is the volume concentration ratio $($VCR$)?$ Give answer with two decimals.

Q$2$:b$)$ What is the polysaccharide concentration $($mg$/$L$)$ in the permeate? Give answer with two decimals.

Q$3$:A $20$ ml sample of the protein production solution is filtered in the laboratory through a filter with a surface area of $6$ cm$2.$ The pressure difference across the filter is $35$ kPa and the filtration time is $5$ min. The compressibility of the filtered protein cake has previously been determined to be s$=0\mathrm{.}4.$

It is desired to filter on a pilot scale in one hour $632$ liters of equivalent protein solution, when the pressure difference across the filter is $82$ kPa. Assuming that the resistance caused by the filter membrane itself is low, how large a filtration area $($in m$2,$ two decimals accuracy$)$ is required in pilot scale filter?