For information and reference only – not to be submitted as your own work.
This is a study extract, not a finished report. It shows how a Level 3 student can set up and check critical path analysis for the Te Kura MXO3042Y1 “Quiz Evening” task for AS 91576, and what the reasoning behind each step looks like. Task 2 is deliberately left at approach level. If you want to see how markers separate Achieved from Excellence, read our companion guide to approaching AS 91576 alongside this page. For wider statistics and modelling support there is also our statistics assignment help page.
What this sample covers
- How to turn a precedence table into an activity-on-node network, including trimming redundant dependencies.
- A forward pass and a backward pass, with earliest and latest start and finish times and float.
- The critical path and the minimum completion time for the committee’s project.
- One possible allocation of tasks to committee members, with the reasoning for the number of members.
- The thinking an Excellence response brings to the two “what if” questions in Task 2.
The table below maps the standard’s wording to what the extract demonstrates. The wording follows the NZQA achievement standard.
| Grade | NZQA wording | What it looks like in this task |
|---|---|---|
| Achieved | Use critical path analysis in solving problems | A correct network, correct times, correct critical path, a workable allocation |
| Merit | Use critical path analysis, with relational thinking | Explains why the allocation works and links results to the quiz evening context |
| Excellence | Use critical path analysis, with extended abstract thinking | Tests the plan against changes (a delay, fewer people) and justifies a strategy with sound reasoning |
Study extract: setting up the network
Step 1: read the precedence table properly
The resource lists ten activities, A to J, each with a duration in weeks and the activities that must finish first. Some of the listed predecessors are redundant. Activity G needs A, E and F, but F already needs A and E, so the only dependency you need to draw into G is F. Trimming these keeps the diagram readable and shows the marker you understand the logic.
| Activity | Task | Weeks | Immediate predecessors (after trimming) |
|---|---|---|---|
| A | Set the date | 1 | None |
| B | Book the venue | 1 | A |
| C | Advertise and sell tickets | 4 | B |
| D | Find a quiz master | 2 | A |
| E | Write questions and answers | 4 | A |
| F | Check answers | 1 | E |
| G | Print recording sheets | 1 | F |
| H | Organise food and drink | 2 | B |
| I | Seek donated prizes | 4 | A |
| J | Set up the venue | 1 | C, D, G, H, I |
In an activity-on-node diagram, each box holds the activity letter and duration. Arrows run from A to B, D, E and I; from B to C and H; from E to F to G; and from C, D, G, H and I into J. Draw A at the far left and J at the far right. Every other box should have at least one arrow in and one out.
Step 2: forward pass, backward pass and float
The forward pass gives the earliest start (ES) and earliest finish (EF): ES is the largest EF among predecessors, and EF = ES + duration. The backward pass starts from the project finish and gives the latest finish (LF) and latest start (LS): LF is the smallest LS among successors. Float is LS − ES.
| Activity | ES | EF | LS | LF | Float |
|---|---|---|---|---|---|
| A | 0 | 1 | 0 | 1 | 0 |
| B | 1 | 2 | 2 | 3 | 1 |
| C | 2 | 6 | 3 | 7 | 1 |
| D | 1 | 3 | 5 | 7 | 4 |
| E | 1 | 5 | 1 | 5 | 0 |
| F | 5 | 6 | 5 | 6 | 0 |
| G | 6 | 7 | 6 | 7 | 0 |
| H | 2 | 4 | 5 | 7 | 3 |
| I | 1 | 5 | 3 | 7 | 2 |
| J | 7 | 8 | 7 | 8 | 0 |
Check one by hand. J cannot start until every predecessor has finished. C finishes at week 6, D at 3, G at 7, H at 4 and I at 5. The largest is 7, so J starts at week 7 and finishes at week 8.
Step 3: the critical path and the minimum time
Critical activities have zero float: A, E, F, G and J. The critical path is A → E → F → G → J, and 1 + 4 + 1 + 1 + 1 = 8, so the minimum completion time is 8 weeks. The question writing chain controls the whole evening.
The near-critical activity is C, ticket sales. It has one week of float, which means a late venue booking would still be fine, but a two-week slip in B or C would not be. A strong response says this in words, not just in a table, because it tells the committee where to watch.
A common error is to treat the longest single task as the critical path. Here C and I are both four weeks long, the same as E, but only E sits on a chain that adds up to 8 weeks.
For comparison, a more complex scheduling example from a different course is in our SARC 321 construction programme sample.
Study extract: allocating tasks to members
How many members are really needed?
Everyone takes part in A and J, so those two activities occupy weeks 0 to 1 and 7 to 8 for all members. The other eight activities must fit between weeks 1 and 7, a window of 6 weeks. Their durations add up to 1 + 4 + 2 + 4 + 1 + 1 + 2 + 4 = 19 person-weeks.
Three members would give only 3 × 6 = 18 person-weeks inside that window. That is one short, so an 8-week finish needs at least four members. This capacity argument is the kind of reasoning that moves a response from Achieved towards Merit, because it explains why, not just what.
One possible allocation
| Member | Tasks (start – finish, weeks) | Reason |
|---|---|---|
| 1 | A (0–1), E (1–5), G (6–7), J (7–8) | Writes the questions; free in week 5 to 6 while answers are checked |
| 2 | A (0–1), D (1–3), H (3–5), F (5–6), J (7–8) | Checks the answers, so is not the question writer, as the brief requires |
| 3 | A (0–1), B (1–2), C (2–6), J (7–8) | Books the venue then sells tickets; finishes C at week 6 with one week spare |
| 4 | A (0–1), I (1–5), J (7–8) | Seeks prizes over four weeks; spare capacity at the end |
Check each member never does two tasks at once and that every precedence is respected. H starts at 3, after B finishes at 2. F starts at 5, once E has finished. This extract stops here: a full submission would still need a labelled network, a clean schedule and a short recommendation written for the organisers.
If you are weighing up how much of this you can do alone, our do my assignment service explains how model answers and guidance are provided.
Task 2: the reasoning, not the answer
A two-week delay to the question writing
Start with the float for E. It is zero, so the 2-week delay passes straight into the project end date. Say which activities move (F, G, J) and which do not (C, D, H, I, which have float or finish early enough). Then propose and test a strategy, such as splitting the question writing between two members. An Excellence response explains the effect on the critical path and whether a different activity becomes critical after the change.
One member fewer
Reuse the capacity argument above with the new member count. Compare the person-weeks available with the work to be done, say what lower bound that gives, and then check whether the precedence constraints allow it. State the new minimum time, and link it back to the quiz evening, for example the effect on ticket sales time.
Further help
If critical path analysis is only one part of a wider workload, you can see how we handle structured written work on our report writing help page, or browse more NZ assignment samples.
About the expert
Olivia Hart holds a Master’s in Applied Mathematics from the University of Otago, New Zealand, and works on mathematics and technical science assignments covering statistics, calculus and applied problem-solving.
References
- Hillier, F. S., & Lieberman, G. J. (2021). Introduction to operations research (11th ed.). McGraw-Hill Education. (Project scheduling with PERT/CPM is covered in the supplementary chapters at www.mhhe.com/hillier11e.)
- Kelley, J. E., Jr., & Walker, M. R. (1959). Critical-path planning and scheduling. Papers presented at the December 1–3, 1959, Eastern Joint IRE-AIEE-ACM Computer Conference, 160–173. https://doi.org/10.1145/1460299.1460318
- New Zealand Qualifications Authority. (2017). Achievement standard 91576, version 2: Use critical path analysis in solving problems. https://www.nzqa.govt.nz/nqfdocs/ncea-resource/achievements/2019/as91576.pdf
- New Zealand Qualifications Authority. (n.d.). Standard 91576: Use critical path analysis in solving problems. https://www.nzqa.govt.nz/ncea/assessment/view-detailed.do?standardNumber=91576
