$3-$ Your supervisor is contemplating excavating an underground primary opening at a mine site where a $36$ m gold vein, dipping at $60$ degrees from the horizontal, outcropping on the surface and open at depth $($i$.$e$.,$ drilling has not reached a definitive end to the deposit$)$ was recently discovered. The purpose of the underground opening is to provide access to a level to be located $1,500$ m below surface. Given the following two alternatives: $(15$ points$)$

I. Vertical shaft access

a$)$ Shaft sinking costs, $6\mathrm{.}1$ m in diam.: $$21,800/$m $($vertical$)$

b$)$ Shaft must be sunk at least $70$ m below targeted level

II$.$ Ramp access

a$)$ Ramp excavation, $5\mathrm{.}0$ m wide x $4\mathrm{.}0$ m high, $-8$ degrees: $$7,450/$ m $($linear$)$

b$)$ Switchback $($turnout$)$ required every $250$ m drop in elevation $($disregard the length of the turnouts in your calculations$).$