The DO in a $17\backslash$deg C river just downstream of a wastewater treatment plant outflow is $2$ mg$/$L$.$ In the river, the deoxygenation rate coefficient kd is $0\mathrm{.}4$ and the reaeration rate coefficient kr is $0\mathrm{.}6.$ The river travels at an average velocity of $4$ km$/$day$.$ The ultimate BOD is $350$ mg$/$L$.$

A$)$ What is the critical DO and how far downstream does it occur?

B$)$ If the minimum permitted DO level after dilution is $5$ mg$/$L$,$ what length of river downstream of the discharge is non$-$compliant?