Q$18$: Select an ASTM A$992($Fy $=50$ksi$-$shape column to support an axial dead load of $200$ kips and a live load of $350$ kips. The column is $25$ ft long and is pinned at both ends in both the strong and weak axes. The column is braced about Y$-$Y axis at mid$-$point. Restrict your selection to a W$-$shape with a nominal depth of approximately $12$ inches. Determine an appropriate section size that satisfies axial strength requirements according to the applicable design specification $($e$.$g$.,$ AISC$).(18$ pts$)$

YOU CAN USE ANY METHOD BUT SHOW YOUR WORK.