Network Flows Case Study
Network Flows Case Study’s
Anthony Ryan Saxon
February 2, 2015
MTH/221
JEFF BABBITT
I decided to write about the Network Flow Case Study. In this paper I will provide examples from the text and provide the theories that fall behind the problems. After explaining the examples I will provide some real world application and some references on them.
Example 1:
You are needing a new A/C in your home and you are looking to save money on the work and on your bill/bills. The A/C technician explains he can save you some money by using some material that was left over from other jobs. As seen in the picture below: Would this work for this application? This would work. The A/C technician is required to know some type of algebra and know how to use it. Knowing this will allow him/her to graph an air flow chart. This would use an isomorphic simple graph so the same number of edges to correspond with the number vertices. This would show that the proper air flow is given from one point to the other point as quickly as possible, this allows for the air to maintain the temperature that you are looking for. Being able to maintain the same temperature would mean less time your unit will run and this saves you money on your bills. This would be a real world application; because the A/C technician has to use math on a daily basis.
Example 2: In this example we will try to stop any traffic on the water way to and from town. This can be done by placing barriers in the water way. But seeing that the river get wider as it gets further away from town, the barriers need to be placed just right to block the water way traffic. As seen in the diagram below:
When placing the barriers, the first thing you want to do is figure out which points to place the barriers. This will allow the use of fewer barriers in this application. I would first start with points G, J, H, and L. This point have a shortest distance between them and would be easier to block. Then if you wanted to
Anthony Ryan Saxon
February 2, 2015
MTH/221
JEFF BABBITT
I decided to write about the Network Flow Case Study. In this paper I will provide examples from the text and provide the theories that fall behind the problems. After explaining the examples I will provide some real world application and some references on them.
Example 1:
You are needing a new A/C in your home and you are looking to save money on the work and on your bill/bills. The A/C technician explains he can save you some money by using some material that was left over from other jobs. As seen in the picture below: Would this work for this application? This would work. The A/C technician is required to know some type of algebra and know how to use it. Knowing this will allow him/her to graph an air flow chart. This would use an isomorphic simple graph so the same number of edges to correspond with the number vertices. This would show that the proper air flow is given from one point to the other point as quickly as possible, this allows for the air to maintain the temperature that you are looking for. Being able to maintain the same temperature would mean less time your unit will run and this saves you money on your bills. This would be a real world application; because the A/C technician has to use math on a daily basis.
Example 2: In this example we will try to stop any traffic on the water way to and from town. This can be done by placing barriers in the water way. But seeing that the river get wider as it gets further away from town, the barriers need to be placed just right to block the water way traffic. As seen in the diagram below:
When placing the barriers, the first thing you want to do is figure out which points to place the barriers. This will allow the use of fewer barriers in this application. I would first start with points G, J, H, and L. This point have a shortest distance between them and would be easier to block. Then if you wanted to