General Mathematics · Unit 4 · Networks and decision mathematics 1 · Trees and minimum connector problems
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A communication network connects seven regional offices. The diagram shows the available fibre-optic links and their installation costs (in thousands of dollars). Determine the minimum total cost required to connect all seven offices.
The diagram shows a network of seven wind turbines (labelled \( A \) to \( G \)) that need to be connected by underground cables. The length (metres) of each possible cable route is shown. Determine the minimum total cable length required to connect all seven turbines.
A telecommunications company plans to connect seven regional offices (labelled \(J\), \(K\), \(L\), \(M\), \(N\), \(P\), and \(Q\)) with fibre-optic cable. The table shows the cost (in thousands of dollars) of installing cable along each possible direct route between offices. Determine the minimum total cost to connect all seven offices and identify which routes should be used.
Determine the total length (km) of the minimum spanning tree for the network of fire trails shown in the diagram.
The table shows the cost (in thousands of dollars) to construct fibre-optic cables between five server hubs labelled \( H \), \( J \), \( K \), \( L \) and \( M \). Determine the minimum total cost to connect all hubs and identify which cables are required.