A three $-$ component mixture at $600$ lbf$/$in$^2($absolute pressure$)$ is fed to a membrane separator with a permeate pressure of $120$ lbf$/$in$^2.$ The mixture has $50\%$ A$,30\%$ B$,$ and $20\%$ C$,$ with permeabilities Q$\_$A $=0\mathrm{.}4,$ Q$\_$B $=0\mathrm{.}1,$ and Q$\_$C $=0\mathrm{.}15,$ all in lb $-$ mole$/$lbf$.$h$.$ Estimate the total flux and the composition of the permeate at the inlet end of the separator. Neglect boundary layer resistances