A school is designing a computer network between five key areas within the school.

The cost of connecting the rooms is shown in the diagram below.
  

1. Complete the spanning tree below that creates the school's network at a minimum cost.  (1 mark)
     

   
    
    

2. What is the minimum cost of the network?  (1 mark)
   

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A factory requires seven computer servers to communicate with each other through a connected network of cables.

The servers, , , , , , and , are shown as vertices on the graph below.
 

 
The edges on the graph represent the cables that could connect adjacent computer servers.

The numbers on the edges show the cost, in dollars, of installing each cable.

1. What is the cost, in dollars, of installing the cable between server and server ?  (1 mark)
   

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2. What is the cheapest cost, in dollars, of installing cables between server and server ?  (1 mark)
   

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3. The computer servers will be able to communicate with all the other servers as long as each server is connected by cable to at least one other server.
   
   1. The cheapest installation that will join the seven computer servers by cable in a connected network follows a minimum spanning tree.
      

       

      Draw the minimum spanning tree on the plan below.  (1 mark) 
       
      
      
       

   2. The factory’s manager has decided that only six connected computer servers will be needed, rather than seven.
      

       

      How much would be saved in installation costs if the factory removed computer server  from its minimum spanning tree network?
      

       

      A copy of the graph above is provided below to assist with your working.  (1 mark)
      
      
      

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