Problem $4.$ Given that $P_u=25$ kips, $M_{ux}=120$ kips$-$ft$,M_{uy}=20$ kips$-$ft$,(KL{)}_x=24ft,(KL{)}_y=L_b=12ft,$

$($a$)$ Select the lightest W$12$ section of Grade $50$ steel for this beam column. Assume as the initial assumptions such that ${}_c{P}_n=300$kips and ${}_b{M}_{ny}=80$kips$-ft.$

$($b$)$ Check the assumptions made in the design process and recheck the section adequacy.