A back tangent with a $+7\%$ grade meets a forward tangent with a $-5\%$ grade on a vertical alignment. A$350$ ft$.$ vertical curve is placed such that BVC is at station $10+35,$ at an elevation of $600$ ft$.$Determine:$($a$)$ curve elevation at station $11+35($b$)$ tangent elevation at PVI$($c$)$ station of crest point$($d$)$ elevation of crest point$($e$)$ elevation of EVC