$.$ A crest vertical curve connects a $+5\mathrm{.}00$ percent grade and a $5\mathrm{.}75$ percent grade. The PVI is at

station $45+50\mathrm{.}00$ at an elevation of $13500\mathrm{.}00$ ft$.$ The design speed is $35$ mi$/$h$.$

Determine:

$($a$)$ The length of the vertical curve

$($b$)$ The station of the BVC $($VPC$)$

$($c$)$ The elevation of the EVC $($VPT$)$

$($d$)$ The elevation of the high point

$($e$)$ The station of the high point

$($f$)$ The elevation of station $45+23\mathrm{.}23$