Edexcel FD1 AS 2019 June — Question 4

Exam BoardEdexcel
ModuleFD1 AS (Further Decision 1 AS)
Year2019
SessionJune
TopicShortest Path

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{103a0bcf-3adf-407c-aa98-a784b0b39bf5-04_577_1357_230_354} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} [The total weight of the network is \(135 + 4 x + 2 y\) ] The weights on the arcs in Figure 1 represent distances. The weights on the arcs CE and GH are given in terms of \(x\) and \(y\), where \(x\) and \(y\) are positive constants and \(7 < x + y < 20\) There are three paths from A to H that have the same minimum length.
  1. Use Dijkstra's algorithm to find \(x\) and \(y\). An inspection route starting at A and finishing at H is found. The route traverses each arc at least once and is of minimum length.
  2. State the arcs that are traversed twice.
  3. State the number of times that vertex C appears in the inspection route.
  4. Determine the length of the inspection route.