$.(20$ points$)$ A segment of $6-$lane freeway is under analysis. The segment is $2$ miles long on an$4\mathrm{.}5\%$ grade with the eastbound being the uphill. Lane width is $11$ ft with $4$ ft shoulder on thenright side. There are $6$ ramps in this segment. Peak hour volume is $4000$ veh$/$h with $3\%$ single$-$unit trucks and $7\%$ tractor$-$trailers. Peak$-$hour factor is $0\mathrm{.}92.$ State DOT$$s goal is to provide a level of service no less than D during the peak $15$ minutes in peak hour. $(1).$Determine if this goal is achievable in the eastbound direction. $(2).$ If yes, how much traffic can be added to the eastbound before level of service drops to the next level.