2 The network below shows 8 towns, \(A , B , \ldots , H\). The number on each edge shows the length of the road, in miles, between towns. During the winter, the council treats some of the roads with salt so that each town can be safely reached on treated roads from any other town. It costs \(\pounds 30\) to treat a mile of road.
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1. 1. Use Prim's algorithm starting from \(A\), showing the order in which you select the edges, to find a minimum spanning tree for the network.
   2. Draw your minimum spanning tree.
   3. Calculate the minimum cost to the council of making it possible for each town to be safely reached on treated roads from any other town.
2. On one occasion, the road from \(C\) to \(E\) is impassable because of flooding. Find the minimum cost of treating sufficient roads for safe travel in this case.
   [0pt] [2 marks]