$(30$ points$)$ A six$-$lane freeway segment has $3$ lanes in each direction and a peak hourly volume of $4500$ vph in each direction. The PHF should be calculated according to the table below. The segment is $0\mathrm{.}375$ mile long with an upgrade of $4\mathrm{.}5\%.$ There is $5\%$ single unit trucks and $5\%$ tractor$-$trailers. Determine the peak $15-$min passenger car equivalent flow rate. If the highway has $11-ft$ lanes, obstructions $3$ ft from the right edge of the traveled pavement, and $1$ interchange for every $2$ miles. What's the level of service of the highway?

$\backslash$table$[[$Time Interval,Traffic Volume$],[4$:$30-4$:$45pm,1050],[4$:$45-5$:$00pm,1100],[5$:$00-5$:$15pm,1250],[5$:$15-5$:$30pm,1100]]$