25 May Question 91) The west-to-east air traffic system passing
Question
91) The west-to-east air traffic system passing through the United States can handle aircraft flows with capacities in hundreds of planes per hour as shown. What is the peak air traffic load (From City 1 to City 5) in aircraft per hour that this system can handle?
92) Find the shortest route from Node 1 to each of the other nodes in the transportation network represented below.
| Route
From Node |
Distance |
| 1 to 2 | 50 |
| 1 to 3 | 100 |
| 2 to 3 | 75 |
| 2 to 5 | 60 |
| 3 to 4 | 80 |
| 3 to 5 | 70 |
| 3 to 6 | 65 |
| 4 to 6 | 200 |
| 5 to 6 | 150 |
93) A logistics company is determining the shortest route to get to a selected final destination. The information on possible paths and distances is given below:
| Route
From Node |
Distance |
| 1 to 2 | 50 |
| 1 to 3 | 100 |
| 1 to 4 | 125 |
| 2 to 4 | 75 |
| 2 to 5 | 180 |
| 3 to 4 | 100 |
| 3 to 5 | 125 |
| 4 to 5 | 170 |
| 4 to 6 | 200 |
| 5 to 6 | 125 |
| 5 to 7 | 100 |
| 6 to 7 | 75 |
94) As part of the planning for a major office development project, it is necessary to install telephone lines to the buildings. Information about the project is given below. The distances are provided in hundreds of feet. Which offices should be connected so that total wiring costs (i.e., total distance) are minimized? What is the total length of this?
| Buildings | Distances (100s ft) |
| 1 to 2 | 4 |
| 1 to 3 | 3 |
| 1 to 4 | 2 |
| 2 to 4 | 4 |
| 3 to 5 | 1 |
| 3 to 6 | 5 |
| 4 to 5 | 3 |
| 4 to 7 | 3 |
| 5 to 7 | 2 |
| 6 to 7 | 6 |
95) Brantley College has decided to “wire” its campus. The first stage in this effort is to install the “backbone,” i.e., to connect all the buildings. The table below gives the distances between the various buildings on campus in hundreds of feet. How should the buildings be connected to minimize the total length of cable? What length of cable is required?
96) Given a network with the following distances:
| From
Node |
To
Node |
Distance |
| 1 | 2 | 4 |
| 1 | 4 | 1 |
| 2 | 3 | 2 |
| 2 | 4 | 3 |
| 3 | 4 | 6 |
| 3 | 5 | 4 |
| 3 | 6 | 2 |
| 4 | 5 | 7 |
| 4 | 7 | 5 |
| 5 | 6 | 5 |
| 5 | 7 | 8 |
| 6 | 7 | 4 |
(a) Determine which nodes should be connected to get the minimum distance flowing from Node 1 through Node 7.
(b) Determine the minimum distance.
97) The east-to-west (City 5 to City 1) air traffic system passing through the United States can handle aircraft flows with capacities in hundreds of planes per hour as shown. What is the peak air traffic load in aircraft per hour from City 5 to City 1 that this system can handle?
98) A water company is analyzing the flow of water through pipes in an office building. The flow capacities are given in the table below. Flow is measured in 100 gallons/hour. What is the maximal flow of water from node 1 to node 5?
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