Q$2.$ A bridge has been constructed between the mainland and an island. The total cost $($excluding tolls$)$ to travel across the bridge is expressed as C $=50+0\mathrm{.}5$V$,$ where V is the number of veh$/$hr and C is the cost$/$vehicle in cents. The demand for travel across the bridge is V $=250010$C$.$

$($a$)$ Determine the volume of traffic across the bridge.

$($b$)$ If a toll of $25$ cents is added, what is the volume across the bridge? What volume would be expected with a $50-$cent increase?

$($c$)$ A tollbooth is to be added, thus reducing the travel time to cross the bridge. The new cost function is C $=50+0\mathrm{.}2$V$.$ Determine the volume of traffic that would cross the bridge.

$($d$)$ Determine the toll to yield the highest revenue for demand and supply function in part $($a$),$ and the associated demand and revenue