SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Networks, GEN1 2024 NHT 40 MC

A project has 10 activities, labelled \(A\) to \(J\). The table below shows the immediate predecessor(s) for each activity. Each activity has a duration of at least one day.

\begin{array}{|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Activity} & \textbf{Immediate}\\
&\textbf{predecessor(s)} \rule[-1ex]{0pt}{0pt}\\
\hline
\rule{0pt}{2.5ex}A \rule[-1ex]{0pt}{0pt}& - \\
\hline
\rule{0pt}{2.5ex}B \rule[-1ex]{0pt}{0pt}& - \\
\hline
\rule{0pt}{2.5ex}C \rule[-1ex]{0pt}{0pt}& A \\
\hline
\rule{0pt}{2.5ex}D \rule[-1ex]{0pt}{0pt}& B \\
\hline
\rule{0pt}{2.5ex}E \rule[-1ex]{0pt}{0pt}& B \\
\hline
\rule{0pt}{2.5ex}F \rule[-1ex]{0pt}{0pt}& D \\
\hline
\rule{0pt}{2.5ex}G \rule[-1ex]{0pt}{0pt}& D, E \\
\hline
\rule{0pt}{2.5ex}H \rule[-1ex]{0pt}{0pt}& C, F \\
\hline
\rule{0pt}{2.5ex}I \rule[-1ex]{0pt}{0pt}& E \\
\hline
\rule{0pt}{2.5ex}J \rule[-1ex]{0pt}{0pt}& G,H \\
\hline
\end{array}

Which one of the following statements about this project is not true?

  1. The earliest starting time of activity \(H\) could be two days.
  2. In the network for this project, there would be a dummy activity from the end of activity \(D\) to the start of activity \(G\).
  3. One of the paths through the network of this project is \(B D G J\).
  4. The latest starting time of activity \(E\) could be three days.
  5. The network for this project would require two dummy activities.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{One strategy: draw a network diagram:}\)
 

\(\text{Earliest starting time of activity \(H\) = 3 days.}\)

\(\Rightarrow A\)

Networks, GEN1 2024 VCAA 40 MC

A project has 15 activities, \(A-O\), that need to be completed.

The directed network that represents this project is shown below.

The activities are not labelled.
 

 

The activity table that could represent this project is
 

 

Show Answers Only

\(B\)

Show Worked Solution

\(\text{A focus are would be the two activities with 4 immediate predecessors.}\)

\(\text{Using trial and error:}\)

♦♦ Mean mark 32%.


  

\(\Rightarrow B\)

Networks, GEN1 2023 VCAA 38 MC

A particular building project has ten activities that must be completed.

These activities and their immediate predecessor(s) are shown in the table below.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Activity} \rule[-1ex]{0pt}{0pt} & \textbf{Immediate predecessor(s)} \\
\hline
A  & - \\
\hline
B  & - \\
\hline
C  & A \\
\hline
 D  & A \\
\hline
E  & B \\
\hline
 F  & D, E \\
\hline
 G  & C, F \\
\hline
 H  & F \\
\hline
 I  & D, E \\
\hline
 J  & H, I \\
\hline
\end{array}

A directed graph that could represent this project is
 

Show Answers Only

\(D\)

Show Worked Solution

\(\text{Activity}\ H\ \text{has only one immediate predecessor,}\ F. \)

\(\text{Eliminate}\ A, B, C\ \text{and}\ E. \)

\(\Rightarrow D\)

NETWORKS, FUR2 2020 VCAA 5

The Sunny Coast cricket clubroom is undergoing a major works project.

This project involves nine activities: `A` to `I`.

The table below shows the earliest start time (EST) and duration, in months, for each activity.

The immediate predecessor(s) is also shown.

The duration for activity `C` is missing.
 

   

The information in the table above can be used to complete a directed network.

This network will require a dummy activity.

  1. Complete the following sentence by filling in the boxes provided.    (1 mark)

    This dummy activity could be drawn as a directed edge from the end of activity to the start of activity  
  1. What is the duration, in months, of activity  `C`?   (1 mark)

  2. Name the four activities that have a float time.   (1 mark)

  3. The project is to be crashed by reducing the completion time of one activity only.

     

    What is the minimum time, in months, that the project can be completed in?    (1 mark)

Show Answers Only
  1. `B\ text{to the start of activity}\ C.`
  2. `text{2 months}`
  3. `A, E, F, H`
  4. `text{17 months}`
Show Worked Solution

a.   `B\ text{to the start of activity}\ C.`

♦♦ Mean mark part (a) 26%.
   

b.   `text{Sketch network diagram.}`

♦ Mean mark part (b) 49%.

 

`text{Duration of Activity C = 2 months}`
  

c.   `text{Critical path:}\   BCDGI`

♦♦ Mean mark part (c) 23%.

`text{Activities with a float time are activities}`

`text{not on critical path.}`

`:. \ text{Four activities are:}\ \ A, E, F, H`
  

d.   `text{Completion time of}\ BCDGI = 20\ text{months}`

♦♦♦ Mean mark part (d) 12%.

`text{Reduce the completion of}\ B\ text{by 3 months to create}`

`text{a new minimum completion time of 17 months.}`

NETWORKS, FUR1 2019 VCAA 7 MC

A project involves nine activities, `A` to `I`.

The immediate predecessor(s) of each activity is shown in the table below.
 

             Activity            Immediate
     predecessor(s)     
  `A` `-`
  `B` `A`
  `C` `A`
  `D` `B`
  `E` `B, C`
  `F` `D`
  `G` `D`
  `H` `E, F`
  `I` `G, H`

 
A directed network for this project will require a dummy activity.

The dummy activity will be drawn from the end of

  1. activity `B` to the start of activity `C`.
  2. activity `B` to the start of activity `E`.
  3. activity `D` to the start of activity `E`.
  4. activity `E` to the start of activity `H`.
  5. activity `E` to the start of activity `F`.
Show Answers Only

`B`

Show Worked Solution

`text(Sketch network diagram:)`
 


 

`text(The dummy activity needs to be drawn)`

`text(from the end of activity)\ B\ text(to the start)`

`text(of activity)\ E.`

`=>  B`

NETWORKS, FUR1 2018 VCAA 7 MC

A project requires nine activities (A–I) to be completed. The duration, in hours, and the immediate predecessor(s) of each activity are shown in the table below.

The minimum completion time for this project, in hours, is

  1. 14
  2. 19
  3. 20
  4. 24
  5. 35
Show Answers Only

`C`

Show Worked Solution

`text(Sketch the network:)`
 

 
`text(Completion time of paths:)`

♦ Mean mark 49%.

`ABEGI = 4 + 3 + 5 + 4 + 3 = 19\ text(hours)`

`ACFGI = 4 + 7 + 2 + 4 + 3 = 20\ text(hours)`

`ADHI = 4 + 2 + 5 + 3 = 14\ text(hours)`
 

`:.\ text{Minimum completion time (critical path) = 20 hours}`

`=> C`

NETWORKS, FUR1 2011 VCAA 7 MC

Andy, Brian and Caleb must complete three activities in total (K, L and M)

The table shows the person selected to complete each activity, the time it will take to complete the activity in minutes and the immediate predecessor for each activity.
 

   

 
All three activities must be completed in a total of 40 minutes.

The instant that Andy starts his activity, Caleb gets a telephone call.

The maximum time, in minutes, that Caleb can speak on the telephone before he must start his allocated activity is

A.    5

B.   13

C.   18

D.   24

E.   34

Show Answers Only

`D`

Show Worked Solution

`text(Maximum speaking time)`

♦♦ Mean mark 33%.
MARKER’S COMMENT: Many students incorrectly answered the earliest starting time, C.

`= 40 – text(duration of)\ M`

`= 40 – 16`

`= 24\ text(minutes)`

`=>  D`

NETWORKS, FUR2 2006 VCAA 3

The five musicians are to record an album. This will involve nine activities.

The activities and their immediate predecessors are shown in the following table.

The duration of each activity is not yet known.
 

NETWORKS, FUR2 2006 VCAA 31
 

  1. Use the information in the table above to complete the network below by including activities `G`, `H` and `I`.  (2 marks)

     

NETWORKS, FUR2 2006 VCAA 32

There is only one critical path for this project.

  1. How many non-critical activities are there?   (1 mark)

The following table gives the earliest start times (EST) and latest start times (LST) for three of the activities only. All times are in hours.


Networks, FUR2 2006 VCAA 3_3

  1. Write down the critical path for this project.   (1 mark)

The minimum time required for this project to be completed is 19 hours.

  1. What is the duration of activity `I`?   (1 mark)

The duration of activity `C` is 3 hours.

  1. Determine the maximum combined duration of activities `F` and `H`.   (1 mark) 
Show Answers Only
  1.  
    networks-fur2-2006-vcaa-3-answer
  2. `5`
  3. `B-E- G-I`
  4. `text(7 hours)`
  5. `text(8 hours)`
Show Worked Solution
a.    networks-fur2-2006-vcaa-3-answer

 

b.   `text(Possible critical paths are,)`

`ADGI, BEGI\ text(or)\ CFHI`

`:.\ text(Non-critical activities)`

`= 9-4 = 5`

 

c.   `text(Critical activities have zero slack time.)`

♦ Mean mark of parts (c)-(e) (combined) was 36%.

`:. A\ text(and)\ C\ text(are non-critical.)`

`:. B-E-G-I\ \ text(is the critical path.)`

 

d.    `text(Duration of)\ \ I` `= 19-12`
    `= 7\ text(hours)`

 

e.   `text(Maximum time for)\ F\ text(and)\ H`

`=\ text(LST of)\ I-text(duration)\ C-text(slack time of)\ C`

`= 12-3-1`

`= 8\ text(hours)`

NETWORKS, FUR1 2015 VCAA 9 MC

The table below shows, in minutes, the duration, the earliest starting time (EST) and the latest starting time (LST) of eight activities needed to complete a project.
 

NETWORKS, FUR1 2015 VCAA 9 MC

 
Which one of the following directed graphs shows the sequence of these activities?

NETWORKS, FUR1 2015 VCAA 9 MCabcde

Show Answers Only

`B`

Show Worked Solution

`=> B`

NETWORKS, FUR2 2013 VCAA 2

A project will be undertaken in the wildlife park. This project involves the 13 activities shown in the table below. The duration, in hours, and predecessor(s) of each activity are also included in the table.
 
NETWORKS, FUR2 2013 VCAA 21
 

Activity `G` is missing from the network diagram for this project, which is shown below.

 
NETWORKS, FUR2 2013 VCAA 22
 

  1. Complete the network diagram above by inserting activity `G`.   (1 mark)

  2. Determine the earliest starting time of activity `H`.   (1 mark)

  3. Given that activity `G` is not on the critical path:
    i.     Write down the activities that are on the critical path in the order that they are completed.   (1 mark)

  4. ii. Find the latest starting time for activity `D`.   (1 mark)

  5. Consider the following statement.
     
    ‘If just one of the activities in this project is crashed by one hour, then the minimum time to complete the entire project will be reduced by one hour.’

    Explain the circumstances under which this statement will be true for this project.   (1 mark)

  6. Assume activity `F` is crashed by two hours.

    What will be the minimum completion time for the project?   (1 mark) 

Show Answers Only
  1.  
    networks-fur2-2013-vcaa-2-answer
  2. `7\ text(hours)`
  3. i. `A-F-I-M`
    ii. `14\ text(hours)`
  4. `text(The statement will only be true if the crashed activity)`
    `text(is on the critical path)\ \ A-F-I-M.`
  5. `text(36 hours)`
Show Worked Solution
a.    networks-fur2-2013-vcaa-2-answer

 

b.    `text(EST of)\ H` `= 4 + 3`
    `= 7\ text(hours)`

 

c.i.   `A-F-I-M`

♦♦ Mean mark of parts (c)-(e) (combined) was 40%.

 

c.ii.  networks-fur2-2013-vcaa-23-answer

`G\ text(precedes)\ I`

`:. text(LST of)\ G = 20-4 = 16\ text(hours)`

`:. text(LST of)\ D = 16-2 = 14\ text(hours)`

  
d.   `text(The statement will only be true if the crashed activity)`

MARKER’S COMMENT: Most students struggled with part (d).

`text(is on the critical path)\ \ A-F-I-M.`
  

e.   `A-F-I-M\ text(is 37 hours.)`

`text(If)\ F\ text(is crashed by 2 hours, the new)`

`text(new critical path is)`

`C-E-H-G-I-M\ text{(36 hours)}`

`:.\ text(Minimum completion time = 36 hours)`

NETWORKS, FUR2 2010 VCAA 4

In the final challenge, each of four teams has to complete a construction project that involves activities `A` to `I`.
 

NETWORKS, FUR2 2010 VCAA 4
 

Table 1 shows the earliest start time (EST), latest start time (LST) and duration, in minutes, for each activity. 

The immediate predecessor is also shown. The earliest start time for activity `F` is missing.

  1. What is the least number of activities that must be completed before activity `F` can commence?   (1 mark)

  2. What is the earliest start time for activity `F`?   (1 mark)

  3. Write down all the activities that must be completed before activity `G` can commence.   (1 mark)

  4. What is the float time, in minutes, for activity `G`?   (1 mark)

  5. What is the shortest time, in minutes, in which this construction project can be completed?   (1 mark)

  6. Write down the critical path for this network.   (1 mark)

Show Answers Only
  1. `2`
  2. `9\ text(minutes)`
  3. `A\ text(and)\ C`
  4. `4\ text(minutes)`
  5. `16\ text(minutes)`
  6. `A-B-D-H`
Show Worked Solution

a.   `2`
  

b.    `text(EST for)\ F` `= 5 + 4`
    `= 9\ text(minutes)`

  
c.   `A\ text(and)\ C`
  

d.    `text(Float time for)\ G` `= 13-9`
    `= 4\ text(minutes)`

 

e.   `text(Shortest construction time)`

`= 5 + 6 + 2 + 3`

`= 16\ text(minutes)`

 

f.   `A-B-D-H`

NETWORKS, FUR2 2011 VCAA 3

A section of the Farnham showgrounds has flooded due to a broken water pipe. The public will be stopped from entering the flooded area until repairs are made and the area has been cleaned up.

The table below shows the nine activities that need to be completed in order to repair the water pipe. Also shown are some of the durations, Earliest Start Times (EST) and the immediate predecessors for the activities.
 

NETWORKS, FUR2 2011 VCAA 3 

  1. What is the duration of activity `B`?   (1 mark)

  2. What is the Earliest Start Time (EST) for activity `D`?   (1 mark)

  3. Once the water has been turned off (Activity `B`), which of the activities `C` to `I` could be delayed without affecting the shortest time to complete all activities?   (1 mark)

It is more complicated to replace the broken water pipe (Activity `E`) than expected. It will now take four hours to complete instead of two hours.

  1. Determine the shortest time in which activities `A` to `I` can now be completed.   (1 mark)

Turning on the water to the showgrounds (Activity `H`) will also take more time than originally expected. It will now take five hours to complete instead of one hour.

  1. With the increased duration of Activity `H` and Activity `E`, determine the shortest time in which activities `A` to `I` can be completed.   (1 mark)

Show Answers Only
  1. `text(2 hours)`
  2. `text(3 hours)`
  3. `text(Activities)\ F and H`
  4. `13\ text(hours)`
  5. `14\ text(hours)`
Show Worked Solution
a.    `text(Duration of)\ B` `= text(EST of)\ C`
    `= 2\ text(hours)`
♦ Mean mark of all parts (combined) was 42%.

  
b.   `text(EST of)\ C = 3\ text(hours)`

  
c.   `text(Activities)\ F and H`

MARKER’S COMMENT: Many students incorrectly included `G` in this answer (note that `G` is not on the critical path).

  
d.   `text(Shortest time)\ (A\ text(to)\ I)`

`= 2 + 1 + 1 + 4 + 4 + 1`

`= 13\ text(hours)`
  

e.   `text(New shortest time)`

`= 2 + 1 + 1 + 4 + 5 + 1`

`= 14\ text(hours)`