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.