Mathematics Chapter 5 Homework Problem 5-30 Flow in Flow out Net flow Sign RHS

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Flows:

From Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Flow out Node Flow in Flow out Net flow Sign RHS

Node 1 0.0 2.0 2.0 1.0 0.0 0.0 0.0 0.0 5.0 Node 1 5.0 5.0 0.0 = 0.0

Node 2 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 2.0 Node 2 2.0 2.0 0.0 = 0.0

Flow balance equations

Problem 5-30

Node 3 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 2.0 Node 3 2.0 2.0 0.0 = 0.0

Node 4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 Node 4 1.0 1.0 0.0 = 0.0

Node 5 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 2.0 Node 5 2.0 2.0 0.0 = 0.0

Node 6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 2.0 Node 6 2.0 2.0 0.0 = 0.0

Node 7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 2.0 Node 7 2.0 2.0 0.0 = 0.0

Capacities:

Node 1 0 2 5 1 0 0 0 0

Node 2 0 0 0 0 2 0 0 0

Node 3 0 0 0 0 2 2 0 0

Node 4 1 0 0 0 0 3 0 4

Node 5 0 2 1 0 0 0 2 0

Node 6 0 0 2 0 0 0 0 4

Node 7 0 0 0 0 2 0 0 2