Use the information below to answer the following questions.
Consider the following maximal flow problem where node 1 is the source and node 6 is the destination.

-Refer to the figure.What is the constraint associated with node 6?
A)X₄₆ + X₅₆ = 0
B)X₄₆ + X₅₆ = 1
C)X₄₆ + X₅₆ - X₆₁ = 1
D)X₄₆ + X₅₆ - X₆₁ = -1
E)X₄₆ + X₅₆ - X₆₁ = 0

Question

Use the information below to answer the following questions.
Consider the following maximal flow problem where node 1 is the source and node 6 is the destination.
 
-Refer to the figure.What is the constraint associated with node 6?
A)X₄₆ + X₅₆ = 0 
B)X₄₆ + X₅₆ = 1 
C)X₄₆ + X₅₆ - X₆₁ = 1 
D)X₄₆ + X₅₆ - X₆₁ = -1 
E)X₄₆ + X₅₆ - X₆₁ = 0

Quizplus · Accepted Answer

Node 6 represents the destination and thus must have a flow of 4 units reaching it. The flow can only come from edges (4,6) and (5,6) and thus the constraint associated with node 6 is X46 + X56 - X61 = 0. Simplifying this equation, we get X46 + X56 = X61, which means the sum of flows entering node 6 (X46 + X56) should be equal to the flow leaving node 6 (X61). Therefore, the correct answer is E) X46 + X56 - X61 = 0.

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