Question

Use the exhaustion of path method to solve the following problem Show all your working by listing each path and weight when exhausting each path, until the maximum flow is found. Solve the following problem using the path of exhaustion method. Make sure you choose the paths from top to bottom to avoid deadlocks. Show all your working by stating each path and its weight An engineer was given the task to study the rainwater drainage in a certain area. The following graph represents the drains and their maximum capacity. What is the maximum flow of rainwater in the drainage system between vertex 1 and vertex 6? 32 23 13 51 40 16 62

Answer 1

3 2 5 イへ Step: onsda path ,→2→5→6 Smallest ehe capacity = 13 Resutont C (1,2) = {3-R = c (2,5) = 32-13 = 19 C(5,6) = 51-13-38 2 38 Smallest edge capocityI capacihes c(i,4)- 62-5 C(4,6)1 o RosuHant 123 51 29 /38

Smallest edge Capoct2 C (3,6)-29-29 :0 19 51 Step 4 Consid the path 1->3-5->6 Smallest ede capocity RosuHant c(,3-92 C(3,5)- a-9-o 5,C): 38-9-29 2. 2 0 /29 Maximum flow: Σ smallest edge capacita in skri 3+11+ 29 19 maximun pessîhle lo is G2,

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