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Networks, STD2 N2 SM-Bank 28

In central Queensland, there are four petrol stations `A`, `B`, `C` and `D`. The table shows the length, in kilometres, of roads connecting these petrol stations.
 


 

  1. Construct a network diagram to represent the information in the table.  (2 marks)

  2. A petrol tanker needs to refill each station. It starts at Station `A` and visits each station.

     

    Calculate the shortest distance that can be travelled by the petrol tanker. In your answer, include the order the petrol stations are refilled.  (2 marks)

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  1.  
  2. `380\ text(km)`
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a.   

 

b.   `text(Shortest Path from)\ A\ (text(visiting all stations))`

`A – B – D – C`

`text(Distance)` `= 170 + 90 + 120`
  `= 380\ text(km)`

Networks, STD2 N2 SM-Bank 25 MC

In a town, there are four cafes `W`, `X`, `Y` and `Z`. The table shows the distances, in metres, of paved footpath connecting the cafes.

A coffee supplier needs to visit each cafe.

What is the shortest distance she needs to walk along the paved footpath if she starts at cafe `W`?

  1. 260 m
  2. 320 m
  3. 330 m
  4. 360 m
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`text(B)`

Show Worked Solution

`text(Possible paths:)`

`W – Z – X – Y = 120 + 70 + 140 = 330\ text(m)`

`W – Z – Y – X = 120 + 100 + 140 = 360\ text(m)`

`W – X – Z – Y = 150 + 70 + 100 = 320\ text(m)`

`W – X – Y – Z = 150 + 140 + 100 = 390\ text(m)`

`=>\ text(B)`

Networks, STD2 N2 SM-Bank 12

The following table shows the travelling time, in minutes, between towns which are directly connected by roads.

A dash indicates that towns are not directly connected.
 


 

  1. Draw a network diagram showing the information in this table.  (2 marks) 

  2. What is the shortest travelling time between A and E?  (1 mark)

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  1.  
         
     
  2. `62\ text(minutes)`
Show Worked Solution
i.  

`text(Important to note that network diagrams)`

`text(do not need to be drawn to scale.)`

 

ii.   `text(One strategy – using Dijkstra’s algorithm:)`
    

 
`:.\ text(Shortest travelling time is the path)\ \ A – D – B – E`

`= 10 + 32 + 20`

`= 62\ text(minutes)`