Analyze the intersection shown in Figure $1$ using the HCM methodology. Clearly provide your results for Parts a and b in a table. $($Suggestion: Using Excel would be helpful in keeping track of the calculations$)$

a$.(12$ pts$)$ Determine the existing $\backslash (\backslash$mathrm$\{$v$\}/\backslash$mathrm$\{$c$\}\backslash )$ ratio, delay, and LOS for each lane group in the intersection. $($Lane groups: EBT, EBR, WBT$,$ WBL$,$ NBL$,$ NBR$)$

b$.(8$ pts$)$ Determine the delay and LOS for:i$)$ each approach and ii$)$ the intersectiof.as a$.$ whols.

c$.(5$ pts$)$ Provide your recommendations for improvements to the signal timing, if your results indicate that improvements are needed.

The following additional information is available for the intersection:

$-$ PHF: $0\mathrm{.}92.$

$-$ Arrival Types: WB: $5$; EB: $2$; NB: $3.$

$-\backslash \%$HV: $\backslash (12\backslash \%\backslash )$ in all movements.

$-$ No need to consider pedestrians as overpasses are provided.

Figure $1.$ Intersection Information for Problem $2.$