$.$ Use Webster's $($optimal cycle length$)$ method to design a two$-$phase signal timing plan for the intersection shown below. All volumes shown are in passenger cars per hour per lane but need to be adjusted for turning movements and the peak hour factor $)=(0\mathrm{.}95.$ We want capacity utilization rate to be no more than $0\mathrm{.}90.$ Assume a loss time of $4$ seconds per phase and a pedestrian walking speed of $3\mathrm{.}5f\frac{t}{sec}.$ The approach speed for all four approaches is $35mph$ and has $0\%$ grade. Design vehicle length is $20ft$ and deceleration is $10f\frac{t}{s^2}.$ Assume PIJR time for drivers is $1\mathrm{.}5sec,$ startup time for pedestrians is $3\mathrm{.}2sec.$ All $4$ crosswalks are $8ft$ wide and assume pedestrian volumes are roughly even between the two crosswalks that serve each directional movement $($NB and SB$,$ for example$).$

Show your final design $($durations of green, yellow, and red for each phase$)$ either in a tabular format or as a time bar. Round all interval times to the nearest $1$ seconds, cycle length should be rounded up to the next $5$ seconds.

$\backslash$table$[[$Phase$,$Lane Group,$\backslash$table$[[$Saturation Flow$],[(ve\frac{h}{h}\frac{?}{ln})$