$(20-$points$)$ A built$-$up box girder is constructed out of $A36$ steel. Assume the section is fully braced in the lateral direction. The top plate is $14"x\frac{1}{2}",$ the web sections are each $14\mathrm{.}5"\frac{3}{4}",$ and the bottom flange is $16"1".$

i$.$ Determine the depth of the elastic neutral axis $(\frac{?}{\text{b}\text{a}\text{r}}(y)),$ the elastic section modulus $(S,$ and the yield moment $(My).$

ii$.$ Determine the depth of the plastic neutral axis $(\frac{?}{\text{b}\text{a}\text{r}}(y)),$ the plastic section modulus $(Z),$ and the plastic moment $(M_P).$

iii. What is the moment capacity of the girder?