Mathematics Standard • Year 12 • Module 6 • Lesson 7
Gantt Charts — Past-Paper Style
Practise HSC Mathematics Standard 2-style writing on Gantt charts — multi-mark short answers and one structured extended response.
1. Short-answer questions
1.1 A project has activities with the following ES, EF and LF: A(0,4,4), B(4,7,7), C(4,6,7), D(7,10,10). Sketch a Gantt chart showing solid bars from ES to EF and a lighter extension for any float. State the critical path. 3 marks Band 3
1.2 The Gantt chart below shows five activities for a project:
A: solid 0 to 3
B: solid 3 to 8
C: solid 3 to 6, lighter extension 6 to 8
D: solid 8 to 11
E: solid 6 to 9, lighter extension 9 to 11
(a) State the project duration.
(b) State the float of activity C and the float of activity E.
(c) List the activities that are in progress on day 7. 3 marks Band 3-4
1.3 A council is upgrading a footpath. The Gantt chart for the 5-day job shows the following activities (all critical, all 1 worker each): Survey (0,1), Concrete cutting (1,2), Concrete pour (2,4), Curing wait (4,5).
(a) State the project duration.
(b) Curing is not "work" — it is a waiting period. On a Gantt chart, is this still drawn as a solid bar? Justify your answer in one sentence.
(c) The council wants a milestone "Pour complete" on day 4. State what symbol is used and where it is placed. 4 marks Band 4
2. Extended response
2.1 A regional NSW vineyard is planning a 12-day grape-pressing operation. Critical path analysis has produced the following ES, EF and LF data:
Pick grapes (Pi): ES = 0, EF = 3, LF = 3
Sort grapes (S): ES = 3, EF = 5, LF = 5
Crush grapes (Cr): ES = 5, EF = 7, LF = 7
Clean equipment (Cl): ES = 5, EF = 6, LF = 7
Press grapes (Pr): ES = 7, EF = 10, LF = 10
Bottle wine (B): ES = 10, EF = 12, LF = 12
(a) Sketch the Gantt chart for the operation, showing solid bars ES → EF and a lighter extension EF → LF for any non-critical activity. (b) State the critical path and project duration. (c) On day 6, both Crush (Cr) and Clean (Cl) need to use the only available forklift. Use the float on Clean (if any) to suggest a single-forklift schedule, and confirm whether the project duration changes. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 3 marks
• 1 mark — chart axes and time scale 0 to 12 correct, with all six activities listed.
• 1 mark — every bar drawn from ES to EF correctly.
• 1 mark — float extension on Clean shown (day 6 to day 7) and no extension drawn on any critical activity.
Part (b) — 2 marks
• 1 mark — critical path stated as Pi → S → Cr → Pr → B.
• 1 mark — project duration stated as 12 days.
Part (c) — 2 marks
• 1 mark — uses Clean's 1-day float to shift it (e.g. Clean runs day 6 → 7) and verifies no overlap with Crush.
• 1 mark — explicit statement that the project duration remains 12 days (the shifted Clean still finishes by its LF = 7).
Your response:
Stuck on (c)? Clean has float = LF − EF = 7 − 6 = 1 day. Shifting Clean to start at day 6 still has it finishing by day 7 — within its LF.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Gantt chart and critical path (3 marks)
Sample response.
A: solid 0–4 (critical, float = 0). B: solid 4–7 (critical, float = 0). C: solid 4–6, extension 6–7 (float = 7 − 6 = 1). D: solid 7–10 (critical, float = 0). Critical path: A → B → D. Project duration = 10 days.
Marking notes. 1 mark — all four bars drawn from ES to EF. 1 mark — float extension shown only on C, no extension drawn on A, B, D. 1 mark — critical path A → B → D explicitly stated.
1.2 — Reading a chart (3 marks)
(a) Project duration = 11 days (last EF on the chart is D ending at day 11).
(b) C's float = 8 − 6 = 2 days. E's float = 11 − 9 = 2 days.
(c) Day 7: B is still running (3–8 solid), E is running (6–9 solid). C's solid bar finishes at day 6, but its float extension covers 6–8 — C is not actively being worked on. Active activities on day 7: B and E (C is in float, not in progress).
Marking notes. 1 mark — duration. 1 mark — both floats correct. 1 mark — correct activities, distinguishing solid bars from float extensions.
1.3 — Footpath upgrade (4 marks)
(a) Project duration = 5 days.
(b) Yes — the bar is still drawn solid because the Gantt chart shows what is happening on the project at that time. Curing is a mandatory time on the timeline (even though no worker is needed), and the next activity cannot start until it finishes.
(c) A diamond placed on the time axis at day 4, labelled "Pour complete".
Marking notes. (a) 1 mark. (b) 1 mark — solid bar, 1 mark — justification (occupies timeline / blocks successors). (c) 1 mark — diamond at day 4.
2.1 — Vineyard pressing operation (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Gantt chart sketch.
Time axis: 0 to 12 days. Activities listed vertically Pi, S, Cr, Cl, Pr, B.
Pi: solid 0–3 (critical). [axes + listing — 1 mark]
S: solid 3–5 (critical).
Cr: solid 5–7 (critical).
Cl: solid 5–6, lighter extension 6–7 (float = 7 − 6 = 1 day). [bars correct ES → EF — 1 mark]
Pr: solid 7–10 (critical).
B: solid 10–12 (critical). [float extension only on Cl, none on criticals — 1 mark]
(b) Critical path and duration.
Critical activities have LF − EF = 0: Pi (0), S (0), Cr (0), Pr (0), B (0). Cl has float = 1, so not critical.
Critical path: Pi → S → Cr → Pr → B. [1 mark]
Project duration = 12 days. [1 mark]
(c) Single-forklift schedule on day 6.
Cr (5–7) and Cl (5–6) currently overlap on day 5–6, both needing the forklift. Cr is critical (no flexibility). Cl has 1 day of float (LF = 7).
Shift Cl to run day 6–7 (using its 1-day float). New schedule: Cr 5–7 alone, then Cl 6–7 overlaps with Cr on day 6 — that still conflicts. Better: Cl runs day 7 only? No — Cl is 1 day duration. With Cl having to start by LF − duration = 7 − 1 = 6 at the latest, the only no-conflict option using float is Cl 6–7, but Cr is still running 5–7. Within Cl's float window (start anywhere from ES = 5 to LS = 6), any placement of Cl overlaps with Cr (which runs 5–7). [1 mark — recognising the float window and identifying the irresolvable overlap]
Conclusion: Cl's 1-day float is not enough to avoid the forklift conflict with Cr. The forklift constraint means Cl must wait until after Cr (start day 7, finish day 8), which is past Cl's LF of 7. This pushes the project: Cl 7–8, then Pr starts at 7 unchanged (Pr's predecessor was Cr). Pr finishes day 10, B finishes day 12. Project duration is unchanged at 12 days because Cl's late finish (day 8) is still earlier than Pr's EF (day 10) and B's start (day 10). [1 mark — explicit duration check confirming 12 days]
Total: 7/7.
Band descriptors for marker.
Band 3: Draws bars but mixes ES/LF positions or omits float extensions. ≈ 3–4 marks.
Band 4: Correct chart with float extension on Cl, identifies critical path but mis-states duration or skips (c). ≈ 5 marks.
Band 5: Full chart, correct path and duration; partial (c) — proposes a shift but does not verify duration. ≈ 6 marks.
Band 6: Complete chart, critical path stated, float used correctly, AND explicit confirmation that project duration is unchanged at 12 days. 7/7.