Column design: A column shown below has ties as transverse reinforcement conforming to ACI $25\mathrm{.}7\mathrm{.}3.$ Assume normal$-$weight concrete with $f_c^{\text{'}}=4000$ and Grade $60$ reinforcement.

$($a$)$ Calculate the theoretical compression strength $P_o$ per ACI$318-19.(10$ points$)$

$($b$)$ Calculate the maximum design axial compression strength $P_{n,\text{m}\text{a}\text{x}}$ of the column. $(10$ points$)$

$($c$)$ Calculate the nominal compressive strength $(P_n)$ if the neutral axis is $6$ in$.$ measured from the right edge of the column. Assume bending is about the $Y$ axis. $(10$ points$)$