3 A theme park has 11 rides, \(A , B , \ldots K\). The network shows the distances, in metres, between pairs of rides. The rides are to be connected by cabling so that information can be collated. The manager of the theme park wishes to use the minimum amount of cabling.
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1. Use Prim's algorithm, starting from \(A\), to find the minimum spanning tree for the network.
2. State the length of cabling required.
3. Draw your minimum spanning tree.
4. The manager decides that the edge \(A E\) must be included. Find the extra length of cabling now required to give the smallest spanning tree that includes \(A E\).