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100114_Solution

# 100114_Solution - shown in above network path by red Step 3...

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:l2-17 The road system around the hotel complex on International Drive (node 1) to Disney World (node 11) in Orlando, Florida, is shown in the network of Figure 12.27. The numbers by the nodes represent the traffic flow in hundreds of cars per hour. What is the maximum flow of cars from the hotel complex to Disney World? P Step 1: we pick the path 1-2-6-9-11. The smallest capacity on this arc is 3. Subtract the capacity from the nodes on this path in the direction of flow and  subtract it from the arcs in the direction opposite to the flow direction. Adjusting the capacities, we get the following network. Step 2: Next, we pick the path 1-3-7-10-11. Smallest capacity on this path is 8. Repeating the above procedure on this path, we get the adjusted flows as

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Unformatted text preview: shown in above network path by red. Step 3: Next, we pick the path 1-4-7-10-11. Smallest capacity on this path is 0. So no adjustments made. 7 1 2 6 9 1 1 3 7 1 1 4 5 8 5 3 1 3 5 3 11 8 9 8 6 6 2 8 2 1 15 4 14 2 Step 4: Pick the path 1-4-8-10-11. The smallest capacity on this path is 2. Repeating the procedure in step 1, we get the adjusted flows as shown in the figure by blue. Step 5. Check if any increase in flow along any path is possible. As there is no more increase possible after step 4, we have arrived at optimal solution. The maximum flow of cars from the hotel to the Disney world is 1300 cars Path flow 1.2.6.9.11 3 1.3.7.10.11 8 1.4.8.10.11 2 Total flow 13 ....
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100114_Solution - shown in above network path by red Step 3...

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