$(10$ pts$)$ A simple three$-$phase traffic signal has three seconds of lost time per phase and the critical movements shown below. $(1)$ Calculate the optimal cycle length. Using the rounded optimal cycle length, $(2)$ find the green, $(3)$ yellow, and $(4)$ all$-$red times for phase $2($W$/$E through movement$)$ only. The posted speed limit is $25mph$ and the lane width is $12ft$ for each lane. Neglect pedestrians.

Critical Lane Groups:

$\backslash$table$[[$Phase$,\frac{O}{{?}_1},\frac{O}{{?}_2},\frac{O}{{?}_3}$