A $24$ ft simple span laterally supported beam is required to carry a total uniformly distributed service load of $8\mathrm{.}0\frac{k}{f}t.$ Determine the lightest, A$992,$ Wshape to carry this load, considering only flexure and the limit state of yielding, if the load is broken down as follows. Use LRFD$.$

a$.$ Live load $=1\mathrm{.}0\frac{k}{f}t$; dead load $=7\mathrm{.}0$kip$\frac{s}{f}t$

b$.$ Live load $=3\mathrm{.}0\frac{k}{f}t$; dead load $=5\mathrm{.}0$kip$\frac{s}{f}t$

c$.$ Live load $=5\mathrm{.}0\frac{k}{f}t$; dead load $=3\mathrm{.}0$kip$\frac{s}{f}t$

d$.$ Live load $=7\mathrm{.}0\frac{k}{f}t$; dead load $=1\mathrm{.}0$kip$\frac{s}{f}t.$