Using both LRFD and ASD methods, select the lightest satisfactory W$-$shape $($ASTM A$992)$ beam section for a simple span of $32$ ft$,$ to carry the following working $($service$)$ loads: Point Dead Load of $+75$ kips and an uplift Point Wind Load of $-30$ kips at mid$-$span of the beam. Beam self$-$weight is not included in the working loads and must be accounted for in the final section. Lateral bracing for the compression flange is provided at the beam ends and at mid$-$span. Use the most appropriate lateral$-$torsional buckling modification factor $($Cb$)$ to calculate the effective moments and use Table $3-10$ in the AISC Manual to find the lightest W$-$Shape.