Question

please explain how you found the answer. None of the chegg answers explain how they got to the answer too well.A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situation is an evacuation starting at the school and ending at the park. The connections between these two locations, plus their capacity and direction, is shown below. с Oak Street 11 Street F А School Park B G Elm Street 2nd Street E A B с D F G Path Capacity E 5 5 25 25 5 10 5 (Round your answer to the nearest whole number.) Maximum Flow 25

Answer 1

The maximum flow is 25. This means that the maximum number of vehicles that can be moved from the school to the park in an emergency is 25.

How is that so?

To find this, we can use the Ford-Fulkerson algorithm. This method is a systematic approach to find the maximum flow in a network. It works by discovery a path from the origin (in this case, the school) to the sink (in this case, the park) that has not utilized its maximum capacity, and therefore shipping as much flow as possible through that way. The process will be repeated if there are no longer paths that maybe used to send flow.

From the problem, it is clear that the course from the school to the park that has the most competency is the path that searches A, C, F, and G. This path has a ability of 25 vehicles. Already you send 25 vehicles through this path, it is filled and you cannot send other vehicles through it.

There are other paths from the school to the park, but they have lower capacities. For example, the path that goes through A, D, and E has a capacity of only 5 vehicles. So, once you send 25 vehicles through the path with the highest capacity, you can only send 5 more vehicles through the next highest capacity path.

Once you have sent as many vehicles as possible through all of the paths, you have reached the maximum flow. In this case, the maximum flow is 25 vehicles.