Southwestern University (SWU), located in the small town of Stephenville, Texas, is experiencing increased interest in its football program no that a big-name coach has been hired. The increase in season ticket sales for the upcoming season means additional revenues, but it also means increased complaints due to the traffic problems associated with the football games. When a new stadium is built, this will only get worse. Marty Starr, SWU’s president, has asked the University Planning Committee to look into this problem.
Based on traffic projections, Dr. Starr would like to have sufficient capacity so that 35,000 cars per hour could travel from the stadium to the interstate highway. To alleviate the anticipated traffic problems, some of the current streets leading from the university to the interstate highway are being considered for widening to increase the capacity. The current street capacities with the number of cars (in 1,000s) per hour are shown in the accompanying figure. Since the major problem will be after the game, only the flows away from the stadium are indicated. These flows include some streets closest to the stadium being transformed into one-way streets for a short period after each game with police officers directing traffic.
Alexander Lee, a member of the University Planning Committee, has said that a quick check of the road capacities in cars per hour that may leave the stadium (node 1) is 33,000. The number of cars that may pass through nodes 2, 3, and 4 is 35,000 per hour, and the number of cars that may pass through nodes 5, 6, and 7 is even greater. Therefore, Dr. Lee has suggested that the current capacity is 33,000 cars per hour. He has also suggested a recommendation be made to the city manager for expansion of one of the routes from the stadium to the highway to permit an additional 2,000 cars per hour. He recommends expanding whichever route is cheapest. If the city chooses not to expand the roads, it is felt that the traffic problem would be a nuisance but would be manageable.
Based on past experience, it is believed that as long as the street capacity is within 2,500 cars per hour of the number that leave the stadium, the problem is not too severe. However, the severity of the problem grows dramatically for each additional 1,000 cars that are added to the streets.
1. If there is no expansion, what is the maximum number of cars that may actually travel from the stadium to the interstate per hour? Why is this number not equal to 33,000, as Dr. Lee suggested?
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?
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