Consider the following flow network. S-V₁-V3 5-V2->V4->E 5-7√2-2V1-V3- G S->V₂V₁ →V₁ ts (12 6,6 V1 10,1 V2 7,7 6,0 3,3 V3 5,2 V4 8,5 5,5 a) Vertex | Flow in V₁ 611 Vz V₂ 2+3 Flow out ㅋ 3+1 5+2 5 (a) Check it is a proper flow, by confirming that the flow out of each internal vertex (v₁, ..., V4) equals the flow in. (b) Find an augmenting path →√√₂ → √n → Va >> Vz ⇒ t 3 State which edges, on your path, have minimum and maximum flow-capacity. (d) Augment the flow. (e) Run the algorithm one more time to find the min-cut, and check that the flow across the cut equals the capacity. capacity of flow is 15 (12+3)

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