Problem #$3(7\mathrm{.}3$W$)[10$ pts$]$

A freeway has a capacity of $7500$ veh$/$h in one direction that has three lanes. In one morning, traffic arrived at $3300$ veh$/$h$.$ At t$=15$ minutes, a crash occurred and blocked all the lanes. At t$=60$ minutes, police opened two lanes. The capacity of two lanes, V$\_2,$ was unknown but the queue disappeared at t$=120$ minutes. Draw the cumulative arrival and cumulative discharge curves versus time and determine V$\_2,$ and the maximum queue length. Hint: convert all the volume and capacity to the unit of vehicles per minute when drawing the curves.