Effluent from metal$-$finishing plants have the potential of discharging undesirable quantities of metal, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal$-$finishing plant has identified a wastewater stream that contains $5\mathrm{.}15wt\%$ chromium $(Cr)$ and devised the following approach to lowering risk and recovering valuable metal. The wastewater stream is fed to a treatment unit that removes $95\%$ of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of $4500kg$ wastewater $\frac{?}{h}.$ If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess $($anything above $4500k\frac{g}{h})$ bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon.

a$)$ Without assuming a basis of calculation, draw and label a flowchart of the process.

b$)$ Wastewater leaves the finishing plant at a rate $=6000k\frac{g}{h}.$ Calculate $($by hand$)$ the flow rate of liquid to the waste lagoon, ${?}_6(k\frac{g}{h}),$ and the mass fraction of $Cr$ in this liquid, $x_6(kgC\frac{r}{k}g.$

c$)$ Repeat the calculations from part b using Excel and Solver.

$($Hint: stream $2$ can have up to $4500k\frac{g}{h}$ of wastewater. A good idea is to design for the maximum flowrate.$)$