Figure 2-1 represents the layout of a new adventure park that is currently being developed. The nodes represent the park entrance (i.e., Park Entrance) and different adventure zones (i.e., S1 to S7). The park entrance and different adventure zones are currently connected by unpaved roads which are represented by the lines shown in Figure 2-1. The number indicated between the nodes represents the length of such unpaved road (in km). Please note that due to construction considerations, the roads may be curved rather than straight, so the mathematical inequalities applicable to the side length of a polygon may not hold.

S6 10 12 S1 S3

8

S7

658 8

S2

7 S5 14 6

9

Park Entrance

15 S4 14 Figure 2-1

(a) The park owner has engaged your company to build a new cycling track that could connect all the nodes (including the park entrance) and the owner is mindful that the construction time and costs are directly proportional to the length of the cycling track. Appraise the total length of cycling track to be built that could minimize the construction time and costs yet allowing all nodes to be connected. Please show your workings.

(17 marks)

(b) As part of the workplace safety risk assessment, the management needs to plan for the quickest path via the unpaved road for the emergency response team who stations at the park entrance to reach a zone (i.e., Zone S1,..., S7) if there is an emergency in the Zone. In particular, Zones S6 and S7 are the most far-flung zones and a jeep will be used if the emergency response team need to reach Zone S6 or S7.

Recommend the route to be taken in order to reach Zone S6 and Zone S7, respectively, in the shortest possible time on the unpaved road. Please show your workings.

Note: (a) and (b) are independent questions, so you do NOT need to consider the

cycling track arrangements here.