A crest curve is being designed to join a $+3\%$ grade to a $-2\mathrm{.}5\%$ grade on a new highway that is

being designed for $55$ mph$.$ There is an existing $24-$in diameter utility pipe that will run

perpendicular to the road at station $54+32\mathrm{.}3$ and centerline elevation $233$ ft$.$ The pipe requires a

minimum clearance of $3\mathrm{.}5$ ft from the top of the pipe to the road. What is the minimum

elevation possible at the PVC$,$ and where will the PVC be located? Include a sketch $($does not

need to be to scale$)$