Problem $2$: $(30$ Points$)$

A multilane highway segment has the following roadway and traffic characteristics:

$1$ mile in length

Undivided

Rolling terrain

$11-$ft lanes

$5-$ft shoulder

$8$ access points

$3190$ two$-$way peak hour volume $($veh$/$h$)$

$,$ Directional split $=\frac{60}{40}$

$PHF=0\mathrm{.}95$

$8\%$ trucks

$BFFS=55m\frac{i}{h}$

a$)$ How many lanes are needed $($peak direction$)$ to accommodate this flow rate with a level of service no worse than B$?$

b$)$ What is the $\frac{v}{c}?$

c$)$ Bonus $(10$ points$)$: How many vehicles can be added to the peak hour flow rate before reaching LOS E$?$