Mathematics Standard • Year 12 • Module 6 • Lesson 7
Gantt Charts — Problem Set
Apply Gantt chart reasoning to real-world scheduling: kitchen renovations, festival builds, school events, software releases and farm work.
Problem 1 — Kitchen renovation Gantt chart
A Sydney builder is scheduling a 5-activity kitchen renovation. Network analysis has produced: Demolition (0,2,2), Plumbing rough-in (2,5,5), Electrical rough-in (2,4,5), Cabinetry (5,9,9), Splashback tiling (4,7,9).
Set up: What are we solving for?
(i) Calculate the float for each activity. 2 marks
(ii) Sketch the Gantt chart, with bars from ES to EF and lighter extensions to LF for any non-critical activity. State the critical path. 3 marks
(iii) The owner phones on day 4 asking which trades are on site. Use your chart to answer, and state the project end day. 2 marks
Stuck? Revisit lesson § Gantt Chart Basics — solid bars run ES → EF, dashed extension runs EF → LF.Problem 2 — Festival main-stage build
A music festival in regional NSW is erecting a main stage. Activities (hours): Truss build (0,4,4), Lighting rig install (4,8,8), PA install (4,7,8), Backdrop hang (4,6,8), Soundcheck (8,10,10).
Set up: What are we solving for?
(i) Calculate the float for each activity and identify the critical path. 2 marks
(ii) Sketch a Gantt chart from hour 0 to hour 10. Use solid bars for critical activities and lighter extensions for float. 2 marks
(iii) Each install crew (Lighting, PA, Backdrop) needs the same forklift driver, who can only assist one crew at a time. Suggest a smoothed schedule using float so no two crews run together. 3 marks
Stuck? Revisit lesson § Resource View — stack bars by resource, then shift the bar with the most float first.Problem 3 — School athletics carnival setup
A high school is setting up for an athletics carnival. Activities (hours): Erect marquee (0,3,3), Mark long-jump pit (0,1,3), Set up timing gates (3,5,5), Set up PA system (3,4,5), Lay finish-line markings (5,7,7).
Set up: What are we solving for?
(i) Identify all critical activities and state the total setup time. 1 mark
(ii) The PE staff want a Gantt chart for the volunteers. Sketch it, with critical bars distinguished from float extensions. 2 marks
(iii) At what time (hour) should a parent volunteer arrive if they only want to help during the PA setup? Justify using your chart. 2 marks
Stuck? Revisit lesson § Gantt Chart Basics — the solid portion of the PA bar shows when that activity is actually scheduled.Problem 4 — App release schedule
A small Sydney software team is shipping an app update. Activities (days): Code feature (0,5,5), Write tests (0,3,5), Internal review (5,7,7), Beta release (7,10,10), Marketing copy (5,6,10), Bug fixes from beta (10,12,12).
Set up: What are we solving for?
(i) Calculate float for each activity. 2 marks
(ii) Sketch the Gantt chart and state the project duration and critical path. 3 marks
(iii) Add a milestone diamond on the chart at the "Internal review complete" point. State the day. 1 mark
Stuck? Revisit lesson § Gantt Chart Basics — milestones are zero-duration events drawn as diamonds at the moment of completion.Problem 5 — Farm harvest planning
A NSW grain farmer is planning a 6-day harvest. Activities (days): Harvest paddock A (0,2,2), Harvest paddock B (0,3,4), Transport A to silo (2,4,4), Transport B to silo (3,5,5), Silo load + seal (5,6,6).
Set up: What are we solving for?
(i) Compute float for each activity. 2 marks
(ii) Sketch the Gantt chart with critical activities solid and others with float extensions. 2 marks
(iii) The farmer only owns one truck — "Transport A" and "Transport B" cannot run simultaneously. Currently they overlap on day 3–4. Use float (if any) to suggest a single-truck schedule. State the new project end day. 3 marks
Stuck? Revisit lesson § Resource View — if no float covers the overlap, sequential running will extend the duration.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Kitchen renovation
Set up. We are calculating float for each activity, drawing the Gantt chart with bars and float extensions, then reading the chart for day 4.
(i) Demolition: 2 − 2 = 0. Plumbing: 5 − 5 = 0. Electrical: 5 − 4 = 1. Cabinetry: 9 − 9 = 0. Splashback: 9 − 7 = 2.
(ii) Demolition solid 0–2. Plumbing solid 2–5. Electrical solid 2–4, extension 4–5. Cabinetry solid 5–9. Splashback solid 4–7, extension 7–9. Critical path: Demolition → Plumbing → Cabinetry.
(iii) Day 4: Electrical (2–4, just finishing) and Splashback (4–7, just starting) — practically a transition. By mid-day 4, only Splashback is active (Electrical complete; Plumbing still running 2–5, so Plumbing also on site). On day 4 the trades on site are Plumbing and Splashback (with Electrical finishing). Project ends on day 9.
Problem 2 — Festival main stage
Set up. We are computing float, drawing the chart, then re-scheduling Lighting/PA/Backdrop so they never overlap because they all need the same forklift driver.
(i) Truss: 0. Lighting: 8 − 8 = 0. PA: 8 − 7 = 1. Backdrop: 8 − 6 = 2. Soundcheck: 0. Critical path: Truss → Lighting → Soundcheck.
(ii) Truss solid 0–4. Lighting solid 4–8. PA solid 4–7, extension 7–8. Backdrop solid 4–6, extension 6–8. Soundcheck solid 8–10.
(iii) Currently Lighting (4–8), PA (4–7) and Backdrop (4–6) all start at hour 4 — three crews need the forklift at once. Suggested smoothing using float: Backdrop hour 6–8 (use its 2 hours of float) and PA hour 7–10? No — PA only has 1 hour float, but if Backdrop runs 6–8 first, then PA can run 4–7 (no change). Cleaner: Lighting 4–8 (critical), Backdrop 4–6 (within float), PA 6–9? PA only has 1 hour float so PA can shift to start at 5 and finish at 8 (still within LF=8). Stagger: Backdrop 4–6, PA 5–8, Lighting 4–8. The forklift is needed at start of each install — stagger the start times by 1 hour to free the driver, keeping Soundcheck on schedule at hour 8.
Problem 3 — Athletics carnival
Set up. We are identifying critical activities, drawing the Gantt for volunteers, then advising when a PA helper should arrive.
(i) Marquee: 3 − 3 = 0. Long-jump: 3 − 1 = 2. Timing gates: 5 − 5 = 0. PA: 5 − 4 = 1. Finish-line: 7 − 7 = 0. Critical activities: Marquee, Timing gates, Finish-line. Total time = 7 hours.
(ii) Marquee solid 0–3. Long-jump solid 0–1, extension 1–3. Timing gates solid 3–5. PA solid 3–4, extension 4–5. Finish-line solid 5–7.
(iii) PA setup runs hour 3 to 4 (its solid bar). A volunteer arriving by hour 3 will catch the whole PA setup. Justification: the solid portion of the bar shows when the work actually happens; the extension is only float (not scheduled work).
Problem 4 — App release
Set up. We are computing float, drawing the Gantt, marking the project duration and critical path, and adding a milestone diamond.
(i) Code: 5 − 5 = 0. Tests: 5 − 3 = 2. Review: 7 − 7 = 0. Beta: 10 − 10 = 0. Marketing: 10 − 6 = 4. Bug fixes: 12 − 12 = 0.
(ii) Code solid 0–5. Tests solid 0–3, extension 3–5. Review solid 5–7. Beta solid 7–10. Marketing solid 5–6, extension 6–10. Bug fixes solid 10–12. Critical path: Code → Review → Beta → Bug fixes. Duration = 12 days.
(iii) "Internal review complete" milestone diamond at day 7 (the EF of Review).
Problem 5 — Farm harvest
Set up. We are computing float, drawing the Gantt, then resolving a one-truck resource conflict.
(i) Harvest A: 2 − 2 = 0. Harvest B: 4 − 3 = 1. Transport A: 4 − 4 = 0. Transport B: 5 − 5 = 0. Silo: 6 − 6 = 0.
(ii) Harvest A solid 0–2. Harvest B solid 0–3, extension 3–4. Transport A solid 2–4. Transport B solid 3–5. Silo solid 5–6. Critical path: Harvest A → Transport A → (waits for Transport B at day 5) → Silo.
(iii) Conflict: Transport A (2–4) and Transport B (3–5) overlap on day 3–4. Transport A is critical (no float) and Transport B is critical (no float). With one truck, run sequentially: Transport A 2–4, then Transport B 4–6 (push back 1 day). This delays Silo by 1 day, so it runs 6–7. New project end = day 7 (was day 6). One day lost because no float covers the conflict.