# System-Optimal

1.A study showed that during the peak-hour commute on two routes connecting a suburb with a large city, there are a total of 5500 vehicles that make the trip. Route 1 is 7 miles long with a 65-mi/h speed limit and route 2 is 4 miles long with a speed limit of 50 mi/h. The study also found that the total travel time on route 2 increases with the square of the number of vehicles, while the route 1 travel time increases two minutes for every 500 additional vehicles added. Determine the system-optimal total travel time (in veh-h).

a) 29.9 b) 1153.5 c) 1364.6 d) 1585.8

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2. Two routes connect an origin–destination pair, with 2500 and 2000 vehicles traveling on routes 1 and 2 during the peak hour, respectively. The route performance functions are t1 = 12 + x1 and t2 = 7 + 2×2, with the x’s expressed in thousands of vehicles per hour and the t’s in minutes. If vehicles could be assigned to the two routes such as to achieve a system-optimal solution, how many vehicle-hours of travel time could be saved?

a) 965.83 b) 970.83 c) 333.33 d) 5.56