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Analyzing the given network for the road capacities, it is easy to see that initially from the node 1 it is possible to send 33000 cars since 15+12+6 = 33. So Dr. Lee was right regarding the number of cars that may go by different routes starting from one spot, but the mistake…
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Download file to see previous pages However, if we analyze the number of cars that travel the road 3-6, we can see that despite the street’s ability to accept 7 thousand cars, there are only 6. The same situation happens on the road 4-8, whose capacity is 8, but it accepts 4 thousand. In total, such difference of both roads gives us the lack of 1+4 = 5 thousands. This means that genuine maximum number of cars that may actually travel from the stadium to the interstate per hour is 33–5 = 28 thousands. These calculations can be easily proved with the help of special statistical program. Hence, QM for Windows gives the following results:
The maximum network flow differs from the forecast of Dr. Lee because a member of the University Planning Committee has not taken into account traffic jams and traffic delays. Due to imperfect distribution of cars among the streets, not all roads are taken by the exact number of cars that such streets are able to accept. For instance, the capacity of the road 1-2 is 12000 meanwhile 15000 cars travel by this route. This mismatch will cause traffic jams and the waste of time. These 3000 cars could easily travel by the road 1-4 without jamming, which capacity allows additional flow of cars.
2. If the cost for expanding a street were the same for each street, which street(s) would you recommend expanding to increase the capacity to 33,000? Which streets would you recommend expanding to get the total capacity of the system to 35,000 per hour?
In case the price for expanding a street is equal for every road, in order to reach the capacity of 33000 cars, I would recommend expanding the road 1-4 so that it could accept 9000 instead of 6000 cars and the road 1-3, which number of cars would increase from 12000 to 14000. In addition, it is essential to expand any or both streets 6-8 and 7-8 because, taking into account that a node 8 can be reached by three roads, ...Download file to see next pagesRead More
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