$(20pts$ A T$-$shape of flexural member is fabricated from plates. Flange plate is $\frac{1}{2}"\frac{71}{2}"$ and a web plate $\frac{3}{8}\text{'}x17\text{'}.$ The yield stress of the steel is $50$ksi.

a$.$ Determine the distance $y$ from the top of the shape to the horizontal elastic neutral axis, and compute the elastic section modulus $S$ and the yield moment $M_y$ with respect to the major principal axis.

b$.$ Determine the distance $y$ from the top of the shape to the horizontal plastic neutral axis, and compute the plastic section modulus $Z$ and the plastic moment $M_p$ with respect to the major principal axis.