Question 3. In a rainforest, there are ten distinct populations of threatened bu

Question

Question 3. In a rainforest, there are ten distinct populations of threatened butterflies. They are all sepa- rated in space, and to visit these sites a forest ranger would need to travel through the rainforest. Travelling through the rainforest can disturb other plants and animals, so it is important to min imise distance travelled. However, sometimes it is necessary for rangers to move around the area on horses. Paths have been constructed joining the butterfly populations according to the figure below, with the lengths given in kilometers. Moving off those paths would be too destructive to the rainforest. 18 4 10 10 12 An invasive ant species has been found in areas nearby, and if these ants reach the butterfly populations without being killed, the butterfly population will go locally extinct in that location Therefore, the ranger wants to be vigilant in checking whether the ants have invaded the butterfly habitat. In the figure below, the ranger lives in a hut at node 1, and the butterfly population node closest to where the ants were found is node 7. Invasion biologists have suggested that node is likely to be invaded first, so monitoring efforts can be focussed there.

Explanation / Answer

a) The shortest path to reach from node 1 to node 7 to have minimum disruptuon is

1-3-5-7 = 22kms

In rest all other paths if you count the distance travelled the above path will be the shortest

Possible straight paths

1-4-6-7 = 24 kms

1-2-5-7 = 32 kms

So our path will be 1-3-5-7 which is of 22kms

b) assuming she starts from node 1 every day to cover all the

Nodes will be

1-3-2-5-6-4-6-7 = 38kms

Rest all other paths are longer than this path.

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