networks 8
Mac trucks
1) He can't start and finish his journey from Greytown without having to repeat any roads. The network is traversable because there are two odd nodes at Lower Hutt and Featherston. So he would need to start say at Featherston then he would finish in Lower Hutt and vice versa.
2) The shortest distance of roads that join all the places he delivers to can be found using Kruskal's algorithm.
GF/15+GM/16+FU/22+UL/20+LW/30+PP/30++PW/35 = 168 km.
3)Drawing the network to show the minimum amount of time to join the places on his route.
Minimum time = FM/5+FG/10+UF/20+ULpae/10+Upo/20+UPae/25+PoW/27 = 117 mins or 1 hr57mins
4) Scenic Value:
Algorithm for scenic value is GM/7+FG/6+UF/4+UPae/5+Upo/4+UL/3+PoW/2 = value of 31
Excellence from scenic value (1 to 7)
Justification
Number of pathways = number of nodes - 1
8 - 1 = 7 pathways connecting all 8 nodes together.
Start with the largest values which are 6 and 7 connecting Greytown to Featherston and Greytown to Martinborough respectively. But connecting Martinborough to Featherston would create a circuit which is not permitted. We can connect Upper Hutt to Paekakariki, a value of 5. The next largest paths have the same value which can be added to the network. They are Featherston to Upper Hutt and Upper Hutt to Porirua. Upper Hutt can be connected to Lower Hutt since Pakakriki connecting Porirua forms a circuit which is not permitted. Finally the 7th path has a value of 2 connecting Porirua to Wellington. This completes the maximum spanning tree for scenic value.
Number of pathways = number of nodes - 1
8 - 1 = 7 pathways connecting all 8 nodes together.
Start with the largest values which are 6 and 7 connecting Greytown to Featherston and Greytown to Martinborough respectively. But connecting Martinborough to Featherston would create a circuit which is not permitted. We can connect Upper Hutt to Paekakariki, a value of 5. The next largest paths have the same value which can be added to the network. They are Featherston to Upper Hutt and Upper Hutt to Porirua. Upper Hutt can be connected to Lower Hutt since Pakakriki connecting Porirua forms a circuit which is not permitted. Finally the 7th path has a value of 2 connecting Porirua to Wellington. This completes the maximum spanning tree for scenic value.
End of the Excellence section
5)The shortest route from Martinborough to Wellington.
Using Dijkstra's Algorithm the shortest distance is 18 + 22 + 20 + 30 = 90 km
NOT IN 2023/4
6) What combination of roads would make the best trip for Mac?
Heaps of solutions here, you can compare by overlaying and seeing which paths are common and go with those. You then need justify why you are choosing some pathways over others and as long as it makes reasonable sense it will be OK. This is called optimisation and is not in your up coming assessment. I will choose the paths that are the most common to please Jack but for any remaining pathways I will choose those that take the shortest time as priority over the other posible options since time is money so they say.
You need to say which paths have been deleted and why.
Heaps of solutions here, you can compare by overlaying and seeing which paths are common and go with those. You then need justify why you are choosing some pathways over others and as long as it makes reasonable sense it will be OK. This is called optimisation and is not in your up coming assessment. I will choose the paths that are the most common to please Jack but for any remaining pathways I will choose those that take the shortest time as priority over the other posible options since time is money so they say.
You need to say which paths have been deleted and why.
Possible solution from another example
7) An earthquake and flooding have resulted in the map landscape being changed, reflected in the table below. Some extra roads have been added to help traffic flow and one road has been made a one way road. Redraw your map to show the changes.
a) Which roads need to be cleaned up first so that people can travel from any town to another.
b) How will Mac get from Wellington to Paekakariki? I'm not sure if this is a miss print as this resource was found on line and there is no marking guide for it.
b) How will Mac get from Wellington to Paekakariki? I'm not sure if this is a miss print as this resource was found on line and there is no marking guide for it.