Question $1(20$ points$).$ Given the following intersection geometry, volume, saturation flow rates, and phase diagram, determine $1)$ the sum of critical lane group flow ratios $(Y_c),2)$ cycle length based on the HCM method with a desired $x_c=0\mathrm{.}90,3)$ effective green time for phase $2$ using Equation $1$ shown below, $4)$ yellow time for phase $2,$ and $5)$ all$-$red time for phase $2.$

$g_i=(\frac{(\frac{v}{s}{)}_{ci}}{Y_c})*G_{te}$

South bound approach: $40m\frac{i}{h}r$; grade $=-2\%$; left$-$turn $w=21\mathrm{.}42ft$

All lanes are $12$ ft wide

Start$-$up lost time $=2\mathrm{.}5s\frac{ec}{?}$ phase; clearance lost time $=1\mathrm{.}0s\frac{ec}{?}$ phase

Exclusive left saturation flow rate $=1700ve\frac{h}{h}\frac{r}{ln}$

Through saturation flow rate $=1800ve\frac{h}{h}\frac{r}{ln}$

Through$-$right saturation flow rate $=1600ve\frac{h}{h}\frac{r}{ln}$

Through$-$left saturation flow rate $=1450ve\frac{h}{h}\frac{r}{ln}$