The unit processes and their corresponding streams as described in the table below are used to produce a biomass wet solid that is to be used in the production of drugs from biomass solution.

$($a$)$ Based on the descriptions in Table $1,$ construct and label the process flow diagram completely by combining $15,000lb\frac{m}{h}r$ fresh biomass solution which contains $30wt\%$ biomass with the filtrate from the filter which is recycled, and then this combined stream is fed to the evaporator.

$($b$)$ By assuming the ratio of fresh biomass solution feed to biomass solid $($Bio$)$ in the filter cake is $4\mathrm{.}0.$ Determine the,

$($i$)$ first step of balance you would use to start solving this problem. Why?

$($ii$)$ flow rate of water evaporated $(lb\frac{m}{h}r)$ and the composition $(\%)$ of biomass solid $($Bio$)$ and solution in the filter cake.

$($iii$)$ flow rate of recycled filtrate $(lb\frac{m}{h}r$

$\backslash$table$[[$Unit Process,Inlet Stream,Outlet Stream $1,$Outlet Stream $2],[$Crystallizer$,\backslash$table$[[$Concentrated biomass$],[$solution containing $0\mathrm{.}4],[$kg Bio$/$kg$]],\backslash$table$[[$Mixture of biomass solution$],[$and pure solid $($Bio$)]],],[$Evaporator$,$Biomass solution,$\backslash$table$[[$Concentrated biomass$],[$solution containing $0\mathrm{.}4$kg$],[$Bio$/$kg$]],$Water $($W$)],[$Filter$,\backslash$table$[[$Mixture of biomass$],[$solution and pure solid$],[($Bio$)]],\backslash$table$[[$Biomass filter cake $($wet$],[$solid$)$ consists of biomass$],[$solid $($Bio$)$ and solution$]],\backslash$table$[[$Filtrate containing$],[0\mathrm{.}35$gBio$/$g$]]]]$