Problem $3$: A four$-$lane freeway $($two lanes in each direction$)$ operates at capacity during the peak hour. It has $11-$ft lanes, $5-$ft shoulders, and there are $3$ ramps within $3$ miles upstream of the segment midpoint and $3$ ramps within $3$ miles downstream of the segment midpoint. The freeway is on rolling terrain and has $10\%$ heavy vehicles with a PHF of $0\mathrm{.}9.$ It is known that $15\%$ of the AADT occurs in the peak hour and the directional factor is $0\mathrm{.}7.$ Determine:

$($a$)$ Heavy vehicle adjustment factor $($b$)$ Free$-$flow speed

$($c$)$ Capacity

$($d$)$ Volume$-$to$-$capacity ratio

$($e$)$ Density and LOS

$($f$)$ AADT

$($g$)$ What is the highest possible value of the heavy vehicle adjustment factor? $($h$)$ If the volume exceeds capacity, what is the LOS?

Note: No need to show calculations for $($g$)$ and $($h$).$