5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9edb5209-4244-4916-b3ee-d77e395e8cab-06_873_739_178_664}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
[The weight of the network is \(20 x + 3\) ]
Figure 4 shows a graph G that contains 8 arcs and 6 vertices.
- State the minimum number of arcs that would need to be added to make G into an Eulerian graph.
- Explain whether or not the route \(\mathrm { A } - \mathrm { C } - \mathrm { F } - \mathrm { E } - \mathrm { C } - \mathrm { D } - \mathrm { B }\) is an example of a path on G.
Figure 4 represents a network of 8 roads in a city. The expression on each arc gives the time, in minutes, to travel along the corresponding road.
You are given that \(x > 1.6\)
A route is required that
- starts and finishes at the same vertex
- traverses each road at least once
- minimises the total time taken
The route inspection algorithm is applied to the network in Figure 4 and the time taken for the route is found to be at most 189 minutes.
Given that the inspection route contains two roads that need to be traversed twice, - determine the range of possible values of \(x\), making your reasoning clear.