AQA D1 2016 June — Question 4

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2016
SessionJune
TopicRoute Inspection

4 Amal delivers free advertiser magazines to all the houses in his village. The network shows the roads in his village. The number on each road shows the time, in minutes, that Amal takes to walk along that road.
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  1. Amal starts his delivery round from his house, at vertex \(A\). He must walk along each road at least once.
    1. Find the length of an optimal Chinese postman route around the village, starting and finishing at Amal's house.
    2. State the number of times that Amal passes his friend Dipak's house, at vertex \(D\).
  2. Dipak offers to deliver the magazines while Amal is away on holiday. Dipak must walk along each road at least once. Assume that Dipak takes the same length of time as Amal to walk along each road.
    1. Dipak can start his journey at any vertex and finish his journey at any vertex. Find the length of time for an optimal route for Dipak.
    2. State the vertices at which Dipak could finish, in order to achieve his optimal route.
    1. Find the length of time for an optimal route for Dipak, if, instead, he wants to finish at his house, at vertex \(D\), and can start his journey at any other vertex.
    2. State the start vertex.