The intersection features a four$-$phase signal, detailing lane groups for each phase, peak hour volumes in vehicles per hour, and saturation flow rates in vehicles per hour, as illustrated in the table below. Please respond to the following questions.

$\backslash$table$[[$Phase$,1,2,3,4],[$Lane Group,EB L$,$WB L$,$EB T$/$R$,$WB T$/$R$,$SB L$,$SB T$/$R$,$NB L$,$NB T$/$R$],[$Peak Hour Volume $(v),245,230,975,1075,255,235,230,215],[$Saturation Flow Rate $($s$),1750,1725,3350,3400,1725,1750,1700,1750]]$

NB$,$SB$,$ EB$,$ WB: North$-,$ South$-,$ East$-,$ and Westbound

$*$L: Left turn

T$/$R: Thru $($straight$)+$ Right Turn

a$.$ Calculate the critical lane group flow ratio, $(\frac{v}{s}{)}_i,$ for each phase

b$.$ Calculate the sum of flow ratios

c$.$ Calculate the minimum cycle length $($Assume the lost time is $5$ seconds per phase and the critical intersection v$/$c ratio $(x_c)$ of $0\mathrm{.}91$ is desired.$)$

d$.$ Calculate the optimal cycle length using the Webster's formular $($Assume the lost time is $5$ seconds per phase$)$

e$.$ Calculate effective green time for each phase using the minimum cycle length

f$.$ Calculate effective green time for each phase using the optimal cycle length