$($Textbook Chapter $6$ Problem $25)$ A simply supported beam spans $32ft$ and carries a uniformly distributed dead load of $1\mathrm{.}8ki\frac{p}{f}t$ plus the beam self$-$weight and a live load of $5\mathrm{.}4ki\frac{p}{f}t.$ Determine the minimum required plastic section modulus and select the lightest$-$weight Wshape to carry the moment. Consider only the limit state of yielding and use A$992$ steel. Design by $($a$)$ LRFD and $($b$)$ ASD.