Moderate -0.5 This is a straightforward recall question testing understanding of the max-flow min-cut theorem. Students only need to know that any cut provides an upper bound on maximum flow (M ≤ cut capacity), requiring no calculation or problem-solving—just direct application of a fundamental theorem from the specification.
1 The network represents a system of pipes.
The number on each arc represents the upper capacity for each pipe in \(\mathrm { cm } ^ { 3 } \mathrm {~s} ^ { - 1 }\)
\includegraphics[max width=\textwidth, alt={}, center]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-02_793_1255_731_395}
The value of the cut \(\{ S , A , B \} \{ C , D , E , F , T \}\) is \(60 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
The maximum flow through the system is \(M \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
What does the value of the cut imply about \(M\) ?
Circle your answer.
\(M < 60 \quad M \leq 60 \quad M \geq 60 \quad M > 60\)
1 The network represents a system of pipes.\\
The number on each arc represents the upper capacity for each pipe in $\mathrm { cm } ^ { 3 } \mathrm {~s} ^ { - 1 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-02_793_1255_731_395}
The value of the cut $\{ S , A , B \} \{ C , D , E , F , T \}$ is $60 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }$\\
The maximum flow through the system is $M \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }$\\
What does the value of the cut imply about $M$ ?
Circle your answer.\\
$M < 60 \quad M \leq 60 \quad M \geq 60 \quad M > 60$
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2020 Q1 [1]}}