A $10$ ft long beam with a uniformly distributed$$ load of $20$ kips has a bending resistance moment $($Mn$)$ of $642$ kip ft$.$ Assume Fy$=50$ ksi.$$

Compute the required plastic section modulus $($Zx$)$

Group of answer choices

$128\mathrm{.}4$ in$^3$

$171\mathrm{.}2$ in$^3$

None of these answers are correct

$154\mathrm{.}1$ in$^3$

$214\mathrm{.}0$ in$^3$