A reverse osmosis system employs a cellulose$-$based membrane to eliminate total dissolved solids $($TDS$)$ from wastewater. The system's properties are provided below.

$\backslash$table$[[$Properties of system$],[$Feed flow rate $=20,000$m$^(3)/$d$,$Flux rate coefficient $($k$\_($w$))=1\mathrm{.}0$a$10^(-6)$m$/$s$/\backslash$bar $],[$Influent TDS $=2,000$g$/$m$^(3),$Mass transfer rate coefficient $($k$\_($i$))=610^(-8)$m$/$s$],[$Permeate TDS $=400$g$/$m$^(3),$Net operating pressure $=2,800$kPa$],[,$Recovery rate $=89\%]]$

Calculate the following:

$($a$)$ The required minimum membrane area $($in $m^2)$ to achieve the desired permeate TDS concentration. $(22$ points$)$

$($b$)$ The rejection rate $(\%).(5$ points$)$

$($c$)$ The concentration of TDS in the concentrate stream $($in $k\frac{g}{m^3}).(10$ points$)$