this is a correction opportunity to get some points back on this exam. it is not an active exam... please help

The process starts with cheese whey, a liquid residue derived from cheese production, containing $6\mathrm{.}7\%$ of total solids $($the remaining is water$).$ Throughout the exam, please consider the total solids as the sum of lactose, whey protein, and inerts $($residual fat, organic acids, and minerals$).$ The total solids within the cheese streams are made of $71\mathrm{.}64\%$ lactose, $17\mathrm{.}91\%$ protein, and $10\mathrm{.}44\%$ inerts, all expressed on a dry basis. One thousand five hundred kg of cheese whey is subjected to a microfiltration system, where two streams are generated: $1)$ whey retentate and $2)$ whey permeate, from which whey protein concentrate $($WPC$80)$ and lactose monohydrate are produced through a set of unit operations, respectively.

In the case of whey retentate, the micro$-$filtration step recovered $95\%$ of the protein and removed $98\%$ of the lactose from the cheese whey, while the inerts found in the whey retentate is $0\mathrm{.}25\%$ on a wet basis. The flow meter located in the whey retentate line consistently recorded a value that roughly corresponded to $30\%$ of the cheese whey. Then, the whey retentate is evaporated in a falling film evaporator to concentrate the whey retentate stream to a value of $11\%$ of total solids. Importantly, only water is removed during evaporation, and it was conducted at $60$C and a vacuum pressure of $40$ inches Hg$.$ The concentrated whey retentate leaving the evaporator is fed in a spray dryer to obtain a powder of $6\%$ water content. A stream of dried and hot air is fed into the drying chamber at $180$C and $5$ bar. The exhausted air leaves the drier at $70$C and $1$ atm of pressure.

The other stream $($whey permeate$)$ derived from the micro$-$filtration contains $98\%$ of lactose, and $5\%$ of protein from the cheese whey, while the concentration of inerts is $0\mathrm{.}45\%.$ Then, the whey permeate is concentrated in a falling film evaporator to obtain a saturated solution of lactose at $80$C$.$ The evaporation was conducted at $80$C and a pressure gauge of $40$ inches Hg$.$ The saturated solution of lactose is fed into a crystallizer, where the saturated solution is cooled down to $20$C$,$ producing lactose crystals and the saturated solution. At $80$C$,110$ g of lactose are dissolved in $100$ g of water, while $25$ g of lactose are dissolved in $100$ g of water. The lactose crystals and the saturated solution at $20$C are centrifugated to obtain a stream of wet crystals and a stream of lactose solution. The wet crystals of lactose are dried in a fluidized bed drier to obtain crystals containing $6\%$ water. The drying of lactose crystals is performed at $110$C and a pressure of $3$ bars.

Please answer the following points:

$1)$ Develop a flow diagram for the entire process $(80$ points$)$

$2)$ Obtain the mass of WPC$80$ produced $(100$ points$)$

$3)$ Obtain the volume of water removed in the evaporation during the WPC$80$ production $(40$ points$)$

$4)$ Obtain the volume of air needed for the drying of WPC$80(40$ points$)$

$5)$ Obtain the mass of lactose crystals produced $(100$ points$)$

$6)$ Obtain the volume of water removed in the evaporation during the lactose production $(40$ points$)$

$7)$ Obtain the volume of air needed for the drying of lactose $(40$ points$)$

$8)$ Obtain the yield of crystals produced with respect to the initial amount of lactose $(40$ points$)$

$9)$ Demonstrate that the process yields a powder containing at least $80\%$ protein $(20$ points