3 A mining company wants to open a new mine in an area where the ground contains a precious metal. The mining company has carried out a survey of the area. The network below shows nodes which represent the entrance to the new mine, \(X\), and the 8 ventilation shafts, \(A , B , \ldots , H\), which have been installed to prevent the build up of dangerous gases underground.
\includegraphics[max width=\textwidth, alt={}, center]{59347089-ea4a-4ee6-b40e-1ab78aa7cdc3-04_846_1228_623_404} Each arc represents a possible underground tunnel which could be mined.
The weight on each arc represents the estimated amount of precious metal in that possible underground tunnel in tonnes. Due to geological reasons, the mining company can only create 8 underground tunnels. All 8 ventilation shafts must be accessible from the entrance of the mine. 3

1. 1. The mining company wants to maximise the amount of precious metal it can extract from the new mine. Determine the tunnels the mining company should use.
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2. (ii) Estimate the maximum amount of precious metal the mining company can extract from the new mine. 3
3. Comment on why the maximum amount of precious metal the mining company can extract from the new mine may be different from your answer to part (a)(ii).
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4. Before the mining company begins work on the new mine, a government survey prevents the mining company drilling the tunnel represented by \(C F\). Determine the effect, if any, the government survey has on your answers to part (a)(i) and part (a)(ii).