Question 15
The flow network shows the capacity (L/min) of each pipe from source S to sink T. A cut is shown by the dashed line.
What is the capacity of the cut shown?
Not quite. You missed A→T: $8 + 4 = 12\text{ L/min}$.
Not quite. You missed both pipes between A and B: $8 + 7 = 15\text{ L/min}$.
That is it. Step through the hints below to see why.
Not quite. You also added the backward pipe B→A: $8 + 4 + 7 + 3 = 22\text{ L/min}$.
Thick solid lines are the pipes the option counts. A dotted line is a backward pipe the option counts. Thin lines are the rest.
Choose an option to draw the pipes it counts and add their capacities.
Counted: S→B 8 and A→B 4.
Sum: $8 + 4 = 12\text{ L/min}$.
Counted: S→B 8 and A→T 7.
Sum: $8 + 7 = 15\text{ L/min}$.
Counted: S→B 8, A→B 4 and A→T 7.
Sum: $8 + 4 + 7 = 19\text{ L/min}$.
Counted: S→B 8, A→B 4, A→T 7 and the backward pipe B→A 3 (dotted).
Sum: $8 + 4 + 7 + 3 = 22\text{ L/min}$.
(A) leaves out A→T, which runs from the source side to the sink side, so 12 L/min is too small.
(B) rightly leaves out B→A but also leaves out A→B, which runs from the source side to the sink side, so 15 L/min is too small.
(C) counts exactly the pipes that run from the source side to the sink side, so the capacity of the cut shown is 19 L/min.
(D) also counts B→A, which runs from the sink side back to the source side, so it does not add to the capacity of the cut.
Try the question first. Choose a hint above when you want one.
Source side $\{\mathrm{S}, \mathrm{A}\}$, sink side $\{\mathrm{B}, \mathrm{T}\}$.
The pipes from the source side to the sink side are S→B 8, A→B 4 and A→T 7.
B→A (3) runs from the sink side back to the source side, so it does not count.
Capacity $= 8 + 4 + 7 = 19\text{ L/min}$
The pipes from the source side $\{\mathrm{S}, \mathrm{A}\}$ to the sink side $\{\mathrm{B}, \mathrm{T}\}$ are S→B 8, A→B 4 and A→T 7. B→A runs back to the source side, so it does not count. The capacity is $8 + 4 + 7 = 19\text{ L/min}$.
Only mark this done when you could do it without help. Reading the solution does not count.
A Tangent Tuition mock exam question. It is not a past QCAA question, and Tangent Tuition is not affiliated with the QCAA.
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