A $\backslash (1\mathrm{.}5^\{\backslash$prime$\}\backslash$times $1\mathrm{.}5^\{\backslash$prime$\}\backslash )$ square pre$-$cast concrete pile is to be driven $60$ ft into the soil profile shown in the figure below. Estimate the following:

$-$ The geotechnical capacity of the individual pile. Check for the maximum geotechnical capacity by API.

$-$ The structural capacity of the individual pile. Use compressive strength of $4$ ksi for the concrete.

$-$ The number of piles required to support a column carrying a dead load of $350$ kips and live load of $100$ kips. Use load factors of $1\mathrm{.}2$ for dead load and $1\mathrm{.}6$ for live load. Use resistance factors of $0\mathrm{.}30$ for both end bearing and skin friction.