4D.3.4-4D.3.5 Multiple sources, sinks and optimal flow rates Quiz: Pearson Edexcel Further Maths, Unit 42

The 20 questions

1. How is a network with multiple sources converted into a single-source network?

   • Add a supersource
   • Add a supersink
   • Merge all vertices
   • Delete source arcs

2. What equals the capacity of the arc from the supersource to a source?

   • Sum of incoming capacities
   • Sum of outgoing capacities
   • Total net flow
   • Maximum capacity value

3. How is a network with multiple sinks converted to a single sink?

   • Remove all original sinks
   • Reverse all sink arcs
   • Connect each to supersink
   • Connect each to supersource

4. What equals the capacity of the arc from a sink to the supersink?

   • Sum of outgoing capacities
   • Total network flow
   • Maximum sink capacity
   • Sum of entering capacities

5. How is a vertex with a restricted capacity modelled in a network?

   • Remove incoming arcs
   • Double the vertex capacity
   • Add a parallel arc
   • Split into two vertices

6. What does a lower capacity on an arc specify?

   • Minimum required flow
   • Zero flow
   • Maximum allowed flow
   • Average flow

7. In a cut calculation with lower capacities, what is subtracted?

   • Backward lower capacities
   • Forward upper capacities
   • Backward upper capacities
   • Forward lower capacities

8. In the network with source S1 joined to A (4) and B (3), source S2 joined to B (5), A to T (6) and B to T (4), what is the capacity of the supersource arc to S1?

   • 4
   • 12
   • 5
   • 7

9. In the same network, what is the maximum flow from the sources to the sink?

   • 10
   • 8
   • 7
   • 12

10. In the same network, what is the capacity of the cut X = {SS, S1, S2, B}?

    • 10
    • 14
    • 12
    • 8

11. Which set X gives the minimum cut in the same network?

    • {SS, S1, S2, A}
    • {SS, S1, S2, A, B}
    • {SS, S1, S2}
    • {SS, S1, S2, B}

12. A supersink T is joined from T1 by arcs of capacity 3 and 2 entering T1. What is the capacity of the arc from T1 to T?

    • 2
    • 6
    • 3
    • 5

13. A vertex B has capacity 4. What is the capacity of the arc joining its two new vertices after splitting?

    • 2
    • 6
    • 4
    • 8

14. An arc from S-side to T-side has upper capacity 8 and lower capacity 2. An arc from T-side to S-side has upper capacity 5 and lower capacity 1. What is the capacity of the cut?

    • 8
    • 13
    • 7
    • 9

15. An arc has upper capacity 10 and lower capacity 4. Between what values can the flow along this arc lie?

    • From 4 to 10 inclusive.
    • From 0 to 4 inclusive.
    • From 0 to 10 inclusive.
    • From 4 to 6 inclusive.

16. Why does the supersource construction leave maximum flow unchanged?

    • Increases network capacity
    • Eliminates bottlenecks
    • Reduces total flow
    • Preserves source capacity

17. In the network with sources S1 and S2 and sink T, the capacity of B to T is reduced to 2. What is the new maximum flow?

    • 10
    • 8
    • 6
    • 4

18. What is the total capacity of the arcs leaving the supersource in the same network?

    • 7
    • 8
    • 10
    • 12

19. Why must lower capacities be subtracted in a cut calculation?

    • They increase net capacity
    • They remove source vertices
    • They equal upper bounds
    • Backward bounds reduce flow

20. Why does splitting a vertex restrict its flow correctly?

    • It doubles the capacity
    • Flow crosses joining arc
    • It removes the vertex
    • It blocks all output

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