A telecommunications company plans to connect six regional data centres with fibre-optic cables. The table below shows the distances, in kilometres, between data centres that can be directly linked. The company will install cables at a cost of \$8{,}500 per kilometre. (a) Determine a minimum spanning tree for the network and state the total length of cable required. (2 marks) (b) Calculate the total cost of installing the minimum spanning tree. (1 mark) (c) The company has received a government grant of \$1{,}450{,}000. Determine whether the grant is sufficient to cover the installation cost. (1 mark) (d) If the company installs an additional link from Centre P to Centre S (65 km), determine the total cost of this expanded network. (1 mark)
General Mathematics · Unit 4 · Networks and decision mathematics 1 · Trees and minimum connector problems
Solve practical problems involving minimum spanning trees, e.g. minimising the length of cable needed to provide power from a single power station to substations in several towns.
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