A lake with $10^6$ m$^3$ water is fed by a pristine river having a flowrate of $15$ m$^3/$s$.$ Effluent from a smelting plant is also discharged into the lake, which contains $250$ mg$/$L nickel and is discharged to the lake at $1\mathrm{.}5$ m$^3/$s$.$ Dust emitted from the smokestack of the plant also settles back into the lake, at a rate of $0\mathrm{.}5$ mg$/$m$^2.$Nickel is removed from water via sedimentation. Nickel forms insoluble precipitates which settle out of water at a rate $($Vs$)$ of $0\mathrm{.}5$ m$/$yr$.$ The surface area of the lake is $1$ x $10^4$ m$^2.$

Find the steady state concentration of nickel in the lake in mg$/$L$.$