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Networks, STD2 N3 2025 HSC 19

The activities and corresponding durations in days for a project are shown in the network diagram.
 

 

  1. Complete the table showing the immediate prerequisites for each activity. Indicate with an \(\text{X}\) any activities without any immediate prerequisites.   (2 marks)

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Activity} \rule[-1ex]{0pt}{0pt} & \text{Immediate prerequisite(s)} \\
\hline
\rule{0pt}{2.5ex} B \rule[-1ex]{0pt}{0pt} &  \\
\hline
\rule{0pt}{2.5ex} E \rule[-1ex]{0pt}{0pt} &  \\
\hline
\rule{0pt}{2.5ex} F \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

  1. Find the critical path for this project AND state the minimum duration for the project.   (2 marks)

  1. The duration of activity \( A \) is increased by 2. Does this affect the critical path for the project? Give a reason for your answer.   (1 mark)

Show Answers Only

a.           

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Activity} \rule[-1ex]{0pt}{0pt} & \text{Immediate prerequisite(s)} \\
\hline
\rule{0pt}{2.5ex} B \rule[-1ex]{0pt}{0pt} & \text{X} \\
\hline
\rule{0pt}{2.5ex} E \rule[-1ex]{0pt}{0pt} & C,D \\
\hline
\rule{0pt}{2.5ex} F \rule[-1ex]{0pt}{0pt} & E \\
\hline
\end{array}

  
b.   \(\text{Critical Path:}\ BDEFH\)

\(\text{Minimum Duration}\ =4+5+5+7+5=26\ \text{days}\)
 

c.   \(\text{If duration of activity \(A\) is increased by 2:}\)

\(\text{The critical path remains unchanged (EST of activity \(E\) remains = 9)}\)

Show Worked Solution

a.   

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Activity} \rule[-1ex]{0pt}{0pt} & \text{Immediate prerequisite(s)} \\
\hline
\rule{0pt}{2.5ex} B \rule[-1ex]{0pt}{0pt} & \text{X} \\
\hline
\rule{0pt}{2.5ex} E \rule[-1ex]{0pt}{0pt} & C,D \\
\hline
\rule{0pt}{2.5ex} F \rule[-1ex]{0pt}{0pt} & E \\
\hline
\end{array}

  
b.   

\(\text{Critical Path:}\ BDEFH\)

\(\text{Minimum Duration}\ =4+5+5+7+5=26\ \text{days}\)
 

c.   \(\text{If duration of activity \(A\) is increased by 2:}\)

\(\text{The critical path remains unchanged (EST of activity \(E\) remains = 9)}\)

Networks, STD2 N3 2024 HSC 39

A project involving nine activities is shown in the network diagram.

The duration of each activity is not yet known.
 

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

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Activity} \rule[-1ex]{0pt}{0pt} & EST & LST \\
\hline
\rule{0pt}{2.5ex} A \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \ 0\ \ \ \ \ \  & \ \ \ \ \ \ 2\ \ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} C \rule[-1ex]{0pt}{0pt} & 0 & 1 \\
\hline
\rule{0pt}{2.5ex} I \rule[-1ex]{0pt}{0pt} & 12 & 12 \\
\hline
\end{array}

  1. What is the critical path?   (1 mark)
  2. The minimum time required for this project to be completed is 19 hours.
  3. What is the duration of activity \(I\)?   (1 mark)

  4. The duration of activity \(C\) is 3 hours.
  5. What is the maximum amount of time that could occur between the start of activity \(F\) and the end of activity \(H\)?   (1 mark)

Show Answers Only

a.   \(\text{Critical Path:}\ BEGI\)

b.   \(\text{Duration of}\ I =7\ \text{hours}\)

c.  \(\text{Max time}\ =8\ \text{hours}\)

Show Worked Solution

a.   \(\text{Activity}\ A\ \text{and}\ C: \ LST \gt EST\)

\(\Rightarrow\ \text{Activity}\ A\ \text{and}\ C\ \text{not on critical path.}\)

\(\text{Critical Path:}\ BEGI\)
 

♦ Mean mark (a) 43%.

b.   \(\text{Duration of}\ I = 19-12=7\ \text{hours}\)
 

c.   \(\text{Since}\ C + F + H + I\ \text{is not a critical path:}\)

\(C + F + H + I = 18\ \text{or less (C.P. = 19 hours)}\)

\(3+F+H+7 = 18\ \text{or less}\)

\(\Rightarrow\ F+H = 8\ \text{or less}\)

\(\therefore\ \text{Max time from start of}\ F\ \text{to end of}\ H = 8\ \text{hours}\)

♦♦♦ Mean mark (c) 10%.

Networks, STD2 N3 2023 HSC 31

A function centre employs staff so that all necessary tasks can be completed between the end of one function and the beginning of the next function.

The network diagram shows the time taken in hours for the tasks that need to be completed.
 


 

  1. Find the TWO critical paths.  (2 marks)

  2. The function centre wants to decrease the length of each critical path by 3 hours. They can do this by hiring more staff to do ONE of the tasks so it takes less time to complete.
  3. For which task should the centre hire more staff, and how long should that task take to ensure all tasks can be completed in 14 hours?  (2 marks) 

Show Answers Only

a.    `HIGC and HIK`

b.    `text{More staff should be hired for task}\ I.`

`text{By decreasing task}\ I\ text{by 3 hours (so it takes 4 hours), the}`

`text{critical path of the network reduces to 14 hours.}`

Show Worked Solution

a.    `text{Scanning both ways:}`
 

`text{Critical paths:}\ HIGC and HIK`

♦ Mean mark (a) 46%.

 
b.   `text{More staff should be hired for task}\ I.`

`text{By decreasing task}\ I\ text{by 3 hours (so it takes 4 hours), the}`

`text{critical path of the network reduces to 14 hours.}`

Mean mark (b) 52%.

Networks, STD2 N3 SM-Bank 50

Roadworks planned by the local council require 13 activities to be completed.

The network below shows these 13 activities and their completion times in weeks.
 

  1. What is the earliest start time, in weeks, of activity `K`?  (1 mark)

  2. How many of these activities have zero float time?  (2 marks)

  3. It is possible to reduce the completion time for activities `A, E, F, L` and `K`.
  4. The reduction in completion time for each of these five activities will incur an additional cost.
  5. The table below shows the five activities that can have their completion time reduced and the associated weekly cost, in dollars.
     
       
  6. The completion time for each these five activities can be reduced by a maximum of two weeks.
  7. The overall completion time for the roadworks can be reduced to 16 weeks.
  8. What is the minimum cost, in dollars, of this change in completion time?  (3 marks)

Show Answers Only
  1. `14 \ text{weeks}`
  2. `7`
  3. `$ 380 \ 000`
Show Worked Solution

a.    `text{Scan forwards:}`

`EST \ (text{activity} \ K)`

`= A \ E \ J`

`= 6 + 5 + 3`

`= 14 \ text{weeks}`
 

b.     `text{Scan backwards:}`

`text{Critical paths:}\ ADGLM\ text(and)\ AEHLM`

`:. \ text{7 activities have no float time:} \ ADEGHLM`
 

c.    `text{There are 9 possible paths}`

`ADGLM\ (19), AEHLM\ (19) , AEIM\ (14)`

`AEJK\ (17), BCEIM \ (13), BCEJK\ (16)`

`BCEHLM\ (18), BCDGLM \ (18), BFK (11)`

`text{Consider the 5 paths with completions over 16 weeks}`

` to \ text{all contain}\ A\ text{or}\ L \ text{or both.}`
  

`text{Consider} \ ADGLM, AEHLM \ (text{contains both} \ A\ text{and} \ L )`

`to \ text{reduce} \ L xx 2 \ ,  A xx 1 \ text{to reach 16 weeks}`

`to \ text{cheaper than} \ L xx 1 \ , \ A xx 2`
  

`text{Consider} \ BCEHLM , BCDGLM\ (text{both contain} \ L \ text{only})`

`to \ text{reduce} \ L xx 2 \ text{to reach 16 weeks}`
 

`text{Consider} \ AEJK \ ( text{contains} \ A \ text{only} )`

`to \ text{reduce} \ A xx 1 \ text{reach 16 weeks}.`
 

`:. \ text{Minimum cost to reduce time to 16 weeks}`

`= 2 xx 120\ 000 + 1 xx  140\ 000`

`= $ 380\ 000`

Networks, STD2 N3 2020 HSC 26

The preparation of a meal requires the completion of all activities `A` to `J`. The network diagram shows the activities and their completion times in minutes.
 


 

  1. What is the minimum time needed to prepare the meal?   (1 mark)

  2. List the activities which make up the critical path for this network.  (2 marks)

  3. Complete the table below, showing the earliest start time and float time for activities `A` and `G`  (2 marks)
     

Show Answers Only
  1. `46 \ text{minutes}`
  2. `C – D – E – F -H – I`
  3.  
Show Worked Solution

a.     `text{Scan forwards and backwards (to answer all parts):}`

♦♦ Mean mark part (a) 31%.
 


 

`text{Minimum time} = 46 \ text{minutes}`
 

b.     `C – D – E – F – H – I`

Mean mark part (b) 51%.

 

c.  `text{Scan backwards (see above):}`

♦♦ Mean mark part (c) 22%.
  

Networks, STD2 N3 2019 FUR2-N 2

The construction of the new reptile exhibit is a project involving nine activities, `A` to `I`.

The directed network below shows these activities and their completion times in weeks.
 


 

  1. Which activities have more than one immediate predecessor?  (1 mark)

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

  3. What is the latest start time, in weeks, for activity `B`?  (1 mark)

Show Answers Only
  1. `D, G and I`
  2. `text(See Worked Solutions)`
  3. `2\ text(weeks)`
Show Worked Solution

a.   `D, G and I`

 

b.   `text(Scanning forwards and backwards:)`
 

​
 

`text(Critical Path:)\ ACDFGI`

 

c.   `text{LST (activity}\ B text{)}` `= 7 – 5`
    `= 2\ text(weeks)`

Networks, STD2 N3 2019 FUR2 3

Fencedale High School is planning to renovate its gymnasium.

This project involves 12 activities, `A` to `L`.

The directed network below shows these activities and their completion times, in weeks.
 


 

The minimum completion time for the project is 35 weeks.

  1. Identify the critical path and state how many activities are on it?  (2 marks)

  2. Determine the latest start time of activity `E`.  (1 mark)

  3. Which activity has the longest float time?  (1 mark)

It is possible to reduce the completion time for activities `C, D, G, H` and `K` by employing more workers.

  1.  The completion time for each of these five activities can be reduced by a maximum of two weeks.

      

    What is the minimum time, in weeks, that the renovation project could take?  (1 mark)

Show Answers Only
  1. `8\ text(activities)`
  2. `12\ text(weeks)`
  3. `text(Activity)\ J`
  4. `29\ text(weeks)`
Show Worked Solution

a.  `text(Scanning forwards and backwards:)`
 

 

 

`text(Critical path:)\ ABDFGIKL`

`:. 8\ text(activities)`
 

b.  `text(LST for activity)\ E = 12\ text{weeks  (i.e. start of 13th week)}`
 

c.   `text(Consider float times of all activities not on critical path.)`

`J-5, H-1, E-1, C-1`

`:.\ text(Activity)\ J\ text(has the largest float time.)`
 

d.   `text(Critical path after reducing)\ CDGHK\ text(by 2 weeks is)`

`ABDFGIKL.`
 

`:.\ text(Minimum time)` `= 2 + 4 + 7 + 1 + 2 + 2 + 5 + 6`
  `= 29\ text(weeks)`

Networks, STD2 N3 SM-Bank 41

The directed network below shows the sequence of activities, `A` to `S`, that is required to complete a manufacturing process.

The time taken to complete each activity, in hours, is also shown.
  

  1. Determine the critical path of this network.   (2 marks)
  2. Identify the activities that have a float time of 10 hours.   (2 marks)

Show Answers Only
  1. `ABEJKOQS`
  2. `text(Activity)\ G, N`
Show Worked Solution

i.   `text(Scanning forwards then backwards:)`
 

 
`text(Critical Path:)\ \ A-B-E-J-K-O-Q-S`
 

ii.    `text(Using the scanned diagram, activity)\ G and N`

`text(have a float time of 10 hours.)`

Networks, STD2 N3 2019 HSC 26

A project requires activities `A` to `F` to be completed. The activity chart shows the immediate prerequisite(s) and duration for each activity.

  1. By drawing a network diagram, determine the minimum time for the project to be completed.  (3 marks)

  2. Determine the float time of the non-critical activity.  (1 mark)

Show Answers Only
  1. `text(15 hours)`
  2. `text(3 hours)`
Show Worked Solution
a.   

 

`text(Scanning forwards:)`

`text(Minimum time = 2 + 6 + 2 + 4 + 1 = 15 hours)`

`text{(Scanning forwards and backwards is highly recommended but not}`

 `text{required in the network diagram.)}`

 

b.   `text(Critical Path is)\ ABDEF.`

♦♦ Mean mark 30%.

`text(Non-critical activity is)\ C.`

`text(Float time)` `= 5 – 2`
  `= 3\ text(hours)`

Networks, STD2 N3 SM-Bank 39

Bianca is designing a project for producing an advertising brochure. It involves activities A-M.

The network below shows these activities and their completion time in hours.
 


 

  1.  What is the earliest starting time of activity J?  (1 mark)

  2.  What is the latest starting time of activity H?  (1 mark)

  3.  What is the float time of activity I?  (1 mark)

  4.  What is the minimum time required to produce the brochure?  (2 marks)

Show Answers Only
  1. `text(11 hours)`
  2. `text(18 hours)`
  3. `text(2 hours)`
  4. `text(34 hours)`
Show Worked Solution

i.   `text(Scanning forwards and backwards)`
 

 

`text{EST (activity}\ J) = 11\ text(hours)`

 

ii.    `text{LST (activity}\ H)` `=\ text{LST}\ (H)-text(weight)\ (H)`
    `= 20-2`
    `=18\ text(hours)`

 

iii.    `text{Float time}\ (I)` `=\ text(LST)\ (I)-text(EST)\ (I)`
    `=12-10`
    `= 2\ text(hours)`

 

iv.   `text(Critical Path is)\ CGJLM`

`:.\ text(Minimum time)` `= 2 + 9 + 6 + 7 + 10`
  `= 34\ text(hours)`

Networks, STD2 N3 SM-Bank 31

Murray is building a new garage. The project involves activities `A` to `L`.
 

 

The network diagram shows these activities and their completion times in days.

  1. Which TWO activities immediately precede activity `G`?  (1 mark)

  2. By completing the diagram shown, calculate the minimum time required to build the new garage.  (2 marks)

  3. Hence, what is the float time for activity `E`?  (1 mark)

Show Answers Only
  1. `text(Activity)\ C\ text(and)\ D.`
  2. `30\ text(days)`
  3. `6\ text(days)`
Show Worked Solution

a.   `text(Activity)\ C\ text(and)\ D.`

 

b.   

`text(Critical path)\ \ A – D – G – L`

`= 1 + 10 + 13 + 6`

`= 30\ text(days)`

 

c.   `text(Float time of Activity)\ E`

`= 14 – 8`

`= 6\ text(days)`

Networks, STD2 N3 SM-Bank 29

The construction of The Royal Easter show involves activities `A` to `L`. The diagram shows these activities and their completion times in days.
 

 
The company contracted to construct it are given a completion deadline of 31 days.

Calculate the float time of Activity `G`.  (3 marks)

Show Answers Only

`8\ text(days)`

Show Worked Solution

`text(Scanning forwards and backwards:)`
 

 
`text(Critical Path is)\ \ A B E J L\ \ text{(29 days)}`

`=>\ text(Critical path is 2 days less than 31 day deadline)`

`:. text(Float time of Activity)\ G` `= (22 – 16) + 2`
  `= 8\ text(days)`

Networks, STD2 N3 EQ-Bank 19

An engineering project requires activities A to G to be completed, as shown in the table.
 


 

The minimum completion time for the project is 25 days and the critical path includes activities B, D, E and F. The float for activity G is two days and the float for activity C is four days.

Find the possible duration for each of the activities A, C, F and G. Include a network diagram in your answer.  (5 marks)

Show Answers Only

`text(Duration of)\ F = 1\ text(day)`

`text(Duration of)\ G = 4\ text(days)`

`text(*Understand why there are many possibilities for the duration of)`

`A and C, text(provided they add up to 20 days and)\ A\ text(is not longer)`

`text{than 7 days (or a new critical path is created)}.`

Show Worked Solution

`text(Sketch the network:)`
 

`text{Critical path information included in the network (where EST = LST)}`

`F\ text(is on critical path ⇒ no float)`

`:.\ text(Duration of)\ F=  25 – 24 = 1\ text(day)`

 

`text(Duration of)\ G` `=\ text(LST of next activity − EST of)\ G – text(float)`
  `= 25 – 19 – 2`
  `= 4\ text(days)`

 

`text(The float of)\ C\ text{is 4 days (given)}`

`:.\ text(Duration of)\ C` `=\ text(LST of)\ F -\ text(EST of)\ C – 4`
  `= 24 -\ text(EST of)\ C – 4`
  `= 20 -\ text(EST of)\ C`

 

`text(EST of)\ C =\ text(Duration of)\ A\ \ (A\ text(has no prerequisites))`

`=>\ text(Duration of)\ A +\ text(Duration of)\ C = 20\ text(days)`

`:.\ text(Possible durations of)\ A\ text(and)\ C\ text(are:)`

`A = 5\ text(days), C = 15\ text(days)`
 

`text(*Understand why there are many possibilities for the duration of)`

`A and C, text(provided they add up to 20 days and)\ A\ text(is not longer)`

`text{than 7 days (or a new critical path is created)}.`

Networks, STD2 N3 EQ-Bank 18

An engineering project requires activities A to G to be completed, as shown in the table.
 


 

The minimum completion time for the project is 40 weeks and the critical path includes activities A, C, E and G. The float for activity F is six weeks and the float for activity D is 9 weeks.

Find the possible duration for each of the activities B, D, F and G. Include a network diagram in your answer.  (5 marks)

Show Answers Only


 

`text(Duration of)\ G = 3\ text(weeks)`

`text(Duration of)\ F = 9\ text(weeks)`

`text(There are many possibilities for the duration of)\ B and D`

`text(provided they add up to 28 weeks and)\ B\ text(is not longer)`

`text{than 10 weeks (new critical path)}.`

Show Worked Solution

`text(Sketch network:)`

`text{Critical path added to network (where EST = LST)}`

`G\ text(is on critical path ⇒ no float)`

`:.\ text(Duration of)\ G = 40-37 = 3\ text(weeks)`

 

`text(Duration of)\ F` `=\ text(40 − EST of)\ F – text(float)`
  `= 40 – 25 – 6`
  `= 9\ text(weeks)`

 

`text(Float of)\ D = 9\ text{weeks (given)}`

`:.\ text(Duration of)\ D` `=\ text(LST of)\ G -\ text(EST of)\ D – 9`
  `= 37 -\ text(EST of)\ D – 9`
  `= 28 -\ text(EST of)\ D`

 

`text(EST of)\ D =\ text(Duration of)\ B\ \ \ (B\ text(has no prerequisites))`

`text(Duration of)\ B +\ text(Duration of)\ D = 28\ text(weeks)`

`:.\ text(Possible durations of)\ B\ text(and)\ D\ text(are:)`

`B = 1\ text(week), D = 27\ text(weeks)`

 

`text(*Understand why there are many possibilities for the duration of)`

`B and D, text(provided they add up to 28 weeks and)\ B\ text(is not longer)`

`text{than 10 weeks (or a new critical path is created)}.`

Networks, STD2 N3 2007 FUR2 4

A community centre is to be built on the new housing estate.

Nine activities have been identified for this building project.

The directed network below shows the activities and their completion times in weeks.

 

  1. Determine the minimum time, in weeks, to complete this project.  (1 mark)

  2. Determine the float time, in weeks, for activity `D`.  (2 marks)

The builders of the community centre are able to speed up the project.

Some of the activities can be reduced in time at an additional cost.

The activities that can be reduced in time are `A`, `C`, `E`, `F` and `G`.

  1. Which of these activities, if reduced in time individually, would not result in an earlier completion of the project?  (1 mark)

The owner of the estate is prepared to pay the additional cost to achieve early completion.

The cost of reducing the time of each activity is $5000 per week.

The maximum reduction in time for each one of the five activities, `A`, `C`, `E`, `F`, `G`, is `2` weeks.

  1. Determine the minimum time, in weeks, for the project to be completed now that certain activities can be reduced in time.  (1 mark)

  2. Determine the minimum additional cost of completing the project in this reduced time.  (1 mark)

Show Answers Only
  1. `19\ text(weeks)`
  2. `5\ text(weeks)`
  3. `A, E, G`
  4. `text(15 weeks)`
  5. `$25\ 000`
Show Worked Solution

a.  `text(Scanning forwards and backwards:)`
 

 
`BCFHI\ \ text(is the critical path.)`

♦ Mean mark of all parts (combined) 40%.
`:.\ text(Minimum time)` `= 4 + 3 + 4 + 2 + 6`
  `= 19\ text(weeks)`

 

b.    `text(EST of)\ D` `= 4`
  `text(LST of)\ D` `= 9`
`:.\ text(Float time of)\ D` `= 9 – 4`
  `= 5\ text(weeks)`

 

c.  `A, E,\ text(and)\ G\ text(are not currently on the critical path,)`

`text(therefore reducing their time will not result in an)`

`text(earlier completion time.)`
 

d.  `text(Reduce)\ C\ text(and)\ F\ text(by 2 weeks each.)`

`text(However, a new critical path created:)\ BEHI\ \ text{(16 weeks)}`

`:.\ text(Also reduce)\ E\ text(by 1 week.)`

`:.\ text(Minimum completion time = 15 weeks)`

 

e.    `text(Additional cost)` `= 5 xx $5000`
    `= $25\ 000`

Networks, STD2 N3 2013 FUR2 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

     

    1. write down the activities that are on the critical path in the order that they are completed  (1 mark)

    2. find the latest starting time for activity `D`.  (1 mark)

  4. Consider the following statement.

     

    ‘If the time to complete just one of the activities in this project is reduced 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)

  5. Assume activity `F` is reduced by two hours.
    What will be the minimum completion time for the project?  (1 mark)

Show Answers Only

a.

networks-fur2-2013-vcaa-2-answer

b.  `7\ text(hours)`

c.i.  `AFIM`

c.ii. `14\ text(hours)`

d.  `text(The statement will only be true if the crashed activity)`
      `text(is on the critical path)\ \ A F I M.`

e.  `text(36 hours)`

Show Worked Solution
a.    networks-fur2-2013-vcaa-2-answer

 

b.  `text(Scanning forwards and backwards:)`

`text(EST for Activity)\ H`

`= 4 + 3`

`= 7\ text(hours)`
 

c.i.   `A F I M`

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

c.ii.  `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 time reduced 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 reduced by 2 hours, the new critical)`

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

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

Networks, STD2 N3 2012 FUR2 2

Thirteen activities must be completed before the produce grown on a farm can be harvested. 

The directed network below shows these activities and their completion times in days.
 


 

  1. Determine the earliest starting time, in days, for activity `E`.  (1 mark)

  2. An activity with zero duration starts at the end of activity `B`.

     

    Explain why this activity is used on the network diagram.  (1 mark)

  3. Determine the earliest starting time, in days, for activity `H`.  (1 mark)

  4. In order, list the activities on the critical path.  (1 mark)

  5. Determine the latest starting time, in days, for activity `J`.  (1 mark)

Show Answers Only
  1. `12\ text(days)`
  2. `F\ text(has)\ B\ text(as a predecessor while)\ G\ text(and)\ H`
    `text(have)\ B\ text(and)\ C\ text(as predecessors.)`
    `text(S)text(ince there cannot be 2 activities called)\ B, text(a zero)`
    `text{duration activity is drawn as an extension of}\ B\ text(to)`
    `B\ text(show that it is also a predecessor of)\ G\ text(and)\ H.`
  3. `15\ text(days)`
  4. `ABHILM`
  5. `25\ text(days)`
Show Worked Solution
a.    `text(EST of)\ E` `= 10 + 2`
    `= 12\ text(days)`
♦ Mean mark of all parts (combined) 47%.

 

b.   `F\ text(has)\ B\ text(as a predecessor while)\ G\ text(and)\ H`

`text(have)\ B\ text(and)\ C\ text(as predecessors.)`

`text(S)text(ince there cannot be 2 activities called)\ B, text(a zero)`

`text{duration activity is drawn as an extension of}\ B\ text(to)`

`text(show that it is also a predecessor of)\ G\ text(and)\ H.`
 

♦♦ “Few students” were able to correctly deal with the zero duration activity in part (c).

c.  `text(Scanning forwards:)`
 

  
`text(EST for)\ H = 15\ text(days)`
 

d.   `text(The critical path is)\ \ ABHILM`
 


 

e.   `text(The shortest time to complete all the activities)`

MARKER’S COMMENT: A correct calculation based on an incorrect critical path in part (d) gained a consequential mark here. Show your working!.

`= 10 + 5 + 4 + 3  + 4 + 2`

`= 28\ text(days)`
 

`:.\ text(LST of)\ J` `= 28 − 3`
  `= 25\ text(days)`

Networks, STD2 N3 2009 FUR2 4

A walkway is to be built across the lake.

Eleven activities must be completed for this building project.

The directed network below shows the activities and their completion times in weeks.
 

NETWORKS, FUR2 2009 VCAA 4
 

  1. What is the earliest start time for activity E?  (1 mark)

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

  3. The project supervisor correctly writes down the float time for each activity that can be delayed and makes a list of these times.

     

    Determine the longest float time, in weeks, on the supervisor’s list.  (1 mark)

A twelfth activity, L, with duration three weeks, is to be added without altering the critical path.

Activity L has an earliest start time of four weeks and a latest start time of five weeks.
 

NETWORKS, FUR2 2009 VCAA 4
 

  1. Draw in activity L on the network diagram above.  (1 mark)
  2. Activity L starts, but then takes four weeks longer than originally planned.

     

    Determine the total overall time, in weeks, for the completion of this building project.  (1 mark)

Show Answers Only
  1. `7`
  2. `BDFGIK`
  3. `H\ text(or)\ J\ text(can be delayed for)`
    `text(a maximum of 3 weeks.)`
  4.  
    NETWORKS, FUR2 2009 VCAA 4 Answer
  5. `text(25 weeks)`
Show Worked Solution

a.   `7\ text(weeks)`

♦ Mean mark of all parts (combined): 44%.

 

b.  `text(Scanning forwards and backwards)`
 

 
`text(Critical Path is)\ BDFGIK`

 

c.   `H\ text(or)\ J\ text(can be delayed for a maximum)`

`text(of 3 weeks.)`
 

d.    NETWORKS, FUR2 2009 VCAA 4 Answer

 

e.   `text(The new critical path is)\ BLEGIK.`

`=>\ text(Activity)\ L\ text(now takes 7 weeks.)`

`:.\ text(Time for completion)`

`= 4 + 7 + 1 + 5 + 2 + 6`

`= 25\ text(weeks)`