Given the speed$-$density relationship $($where $$ is in mph and $$ is in vehicles per mile$)$:

$=0\mathrm{.}001(250)!2$

Please calculate the following:

$($a$)$ Free$-$flow speed $(5$ points$)$

$($b$)$ Jam density $(10$ points$)$

$($c$)$ Speed and density at maximum flow $(15$ points$)$

$($d$)$ Lane capacity $(5$ points