| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Find missing flow values |
| Difficulty | Easy -1.2 This is a straightforward network flow question requiring only conservation of flow at nodes to find missing values, then inspection to identify maximum flow. Part (a) involves simple arithmetic (flow in = flow out), and part (b) requires recognizing a cut. This is routine D1 material with no problem-solving insight needed, making it easier than average A-level questions. |
| Spec | 7.04f Network problems: choosing appropriate algorithm |
1.
\begin{figure}[h]
\begin{center}
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{4bbe6272-3900-42de-b287-599638ca75e4-02_753_1575_486_255}
\end{center}
\end{figure}
Figure 1 shows a directed, capacitated network where the number on each arc is its capacity. A possible flow is shown from $S$ to $T$ and the value in brackets on each arc is the flow in that arc.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $x , y$ and $z$.
\item Find, by inspection, the maximal flow from $S$ to $T$ and verify that it is maximal.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q1 [5]}}