$($A$)$ An activated sludge system is to he used for secondary treatment of $15000$m $^3/$ d of municipal wastewater. After primary clarification, the BOD is $100$ mg$/$L$,$ and it is desired to have not more than $5$ mg$/$l$.$ soluble BOD in the effluent. A completely mixed reactor is to be used, and pilot$-$plant analysis has established the following kinetic values: Y $=0\mathrm{.}5$kg $/$ k $*$ g$\_\{$i$\}$ ka$=0\mathrm{.}05$ d Assuming an MISS concentration of $3200$ mg$/$L and an underflow concentration of $11000$mg $/$ L from the secondary clarifier, determine $(1)$ the volume reactor, $(2)$ the mass and volume of solids that must be wasted each day, and $(3)$ the recycle ratio.