$2)$ Design the lightest W$-$shape beams to support a $\backslash (150-\backslash$mathrm$\{$mm$\}\backslash )$ thick$-$reinforced concrete slab as shown. The beams are simply supported, are $2\mathrm{.}20$ m on center, and span $12$ m $.$ The service live load on the slab is $6\mathrm{.}0$ kPa $.($Assume the unit weight of reinforced concrete to be $\backslash (23\mathrm{.}5\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).)$