An intersection has a $3-$phase signal with the movements allowed in each phase and corresponding analysis and saturation flow rates shown in the following table:

$\backslash$table$[[$Phase$,1,,2,,,],[\backslash$table$[[$Allowed$],[$Movements$]],$EB L$,$WB L$,$EBT$/$R$,\backslash$table$[[$WB$],[$T$/$R$]],$SB L$,$SB T$/$R$],[\backslash$table$[[$Analysis$],[$flow rate, v$],[($veh$/$hr$)]],245,230,975,1030,255,235],[\backslash$table$[[$Saturation$],[$flow rate,s$],[($veh$/$hr$)]],1750,1725,3350,3400,1725,1750],[(\frac{v}{s}{)}_i,,,,,,]]$

a$.$ Circle the critical lane groups based on the v$/$s ratios i$.$e$.,$ flow ratios for each phase

$(10$ points$)$

b$.$ Calculate the sum of flow ratios for the critical lane groups $(10$ points$)$

${\displaystyle \underset{i=1}{\overset{n}{}}}(\frac{v}{s}{)}_{ci}=,\mathrm{.}140+\mathrm{.}303+\mathrm{.}148=0\mathrm{.}591$

c$.$ If the lost time per phase is $5$ seconds and a critical intersection v$/$c of $0\mathrm{.}85$ is desired, calculate the minimum cycle length $C_{\text{m}\text{i}\text{n}}$ and the optimal cycle length Copt for the intersection.

points$)$