Network Flows Case Study
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. 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 add more protection to the town you could place more barriers at points D, E, and F. Now in a real life application this could be used in something as the military blocking or slowing down the traffic going on and if the base.
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Example 3: Employers and Employees Employers Department 1 Department 2 3 4 Max # area Wanted Yes No NO # Area Needed In this example the table shows where an employer was asked to hire more employees in order to cover 100 departments with 30 different areas. Each new employee would work in areas 1, 2, and 3. The area assigned to the employee would be determined by the employer him/herself. The table above givens an example of how it will go. Then the overall question would be how the assigned areas would be split up.
When it comes to converting the table above into a graph to the answer, I am at a little bit off loss. The employee numbers 1, 2, and 3 would then be converted into vertices ODL , DO, and DO and the different areas into AY , AZ and AY which is shown in the diagram below: In the diagram you have to replace the G's with Do's and the CSS with the Ass. Believe the assigned areas would be given to the employees by the employer. An employer would be assign to an employee by random. The employee would follow the employer's number through the graph.
This would tart in area 1 and continue on through 3. If you have 100 employers and 30 employees they would be assigned in areas as 34, 33, and 33 this would allow all areas to be covered and the jobs completed in a timely manner. In this paper I have provided examples of networking flow charts to the best of my knowledge. This type of flow chart shows the way things can flow and the way you can block the flow of information or even water or air. You can apply this to many of different area's in life. If you can imagine it, I am sure it will work for you.
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