Mathematics Standard • Year 12 • Module 6 • Lesson 2
Activity Networks and Precedence Tables — Problem Set
Apply precedence-table building and reading to realistic Australian projects: a house construction, a research study, a wedding plan, a software release and a school musical.
Problem 1 — House construction (Western Sydney)
A builder lists the activities for a house build (days):
Site prep SP(4) — no predecessor. Foundation FN(6) — needs SP. Framing FR(8) — needs FN. Roofing RF(5) — needs FR. Plumbing rough PL(4) — needs FR. Electrical rough EL(3) — needs FR. Drywall DW(6) — needs PL and EL. Painting PT(4) — needs DW and RF.
Set up: What are we solving for?
(i) Build the precedence table (activity, duration, immediate predecessors) for all eight activities. 2 marks
(ii) Identify the start activity, the finish activity and any pairs of activities that can run in parallel after Framing finishes. 2 marks
(iii) The site supervisor proposes scheduling RF and DW at the same time. Use the precedence table to decide whether this is allowed. Give one short reason. 1 mark
Stuck? Revisit lesson § Building Precedence Tables — RF and DW depend on different chains, so look at when each can start, not just whether they share a predecessor.Problem 2 — University research study (Adelaide)
A research team lists the activities for a 5-week study (days):
Literature review LR(8) — no predecessor. Ethics approval EA(10) — no predecessor. Design experiment DE(3) — needs LR and EA. Recruit participants RP(7) — needs EA. Run trial RT(12) — needs DE and RP. Analyse data AD(6) — needs RT. Write report WR(5) — needs AD.
Set up: What are we solving for?
(i) Build the full precedence table. 2 marks
(ii) Identify all start activities and the finish activity. 1 mark
(iii) The team asks: "Can LR and RP be done in parallel?" Use the table to give a yes/no answer with one short reason. 2 marks
Stuck? Revisit lesson § Reading Tables — "parallel" requires that neither activity be (directly or indirectly) waiting on the other.Problem 3 — Wedding planning (Hunter Valley)
A wedding planner lists tasks (weeks):
Set date SD(1) — no predecessor. Book venue BV(2) — needs SD. Send invites SI(3) — needs BV. Order flowers OF(2) — needs BV. Choose catering CC(2) — needs BV. Final confirmations FC(1) — needs SI and OF and CC.
Set up: What are we solving for?
(i) Build the precedence table. 2 marks
(ii) Identify which three activities form a parallel set after BV finishes. 1 mark
(iii) The planner suggests starting OF before BV is signed. State the rule this breaks and explain in one sentence why this should not be done. 2 marks
Stuck? Revisit lesson § Reading Tables — every activity except start activities must wait for ALL its immediate predecessors.Problem 4 — Software release (Sydney start-up)
A start-up plans a release. Tasks (days):
Specification SP(5) — no predecessor. UI design UI(4) — needs SP. Backend code BE(8) — needs SP. Frontend code FE(6) — needs UI. Integration testing IT(3) — needs BE and FE. Documentation DC(2) — needs SP. User-acceptance UA(2) — needs IT and DC. Release RL(1) — needs UA.
Set up: What are we solving for?
(i) Build the precedence table. 2 marks
(ii) List every activity that depends only on SP (i.e. has SP as its sole predecessor). These are the activities that can all begin once SP finishes. 2 marks
(iii) A junior dev claims "DC can start before SP is finished because writing docs is independent of the spec". State which rule of precedence tables this claim breaks and write a one-line correction. 2 marks
Stuck? Revisit lesson § Reading Tables — if SP is in DC's predecessor column, DC must wait for SP to finish.Problem 5 — School musical production (regional NSW)
A drama teacher lists tasks for the school musical (weeks):
Choose script CS(1) — no predecessor. Auditions AU(2) — needs CS. Cast list CL(1) — needs AU. Rehearsals RH(8) — needs CL. Build set BS(6) — needs CS. Make costumes MC(5) — needs CL. Tech run TR(1) — needs RH and BS and MC. Opening night ON(1) — needs TR.
Set up: What are we solving for?
(i) Build the precedence table. 2 marks
(ii) State the start activity and the finish activity. Then list every activity that can run in parallel with Rehearsals (RH). 2 marks
(iii) Suppose the teacher mistakenly writes BS as "BS(6, CL)" instead of "BS(6, CS)". Explain in one sentence what would change about which activities could start at the same time, and whether the new table is still consistent with the description. 2 marks
Stuck? Revisit lesson § Building Precedence Tables — moving an activity's predecessor later in the chain delays when it can start.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — House construction
Set up. We are building the precedence table for the house and then identifying start, finish, and parallel activities.
(i) SP(4, —), FN(6, SP), FR(8, FN), RF(5, FR), PL(4, FR), EL(3, FR), DW(6, PL and EL), PT(4, DW and RF).
(ii) Start = SP. Finish = PT. After FR finishes, RF, PL and EL all share predecessor {FR} and can run in parallel.
(iii) Yes — RF and DW CAN run at the same time, because RF needs only FR while DW needs PL and EL. Once PL and EL are finished, DW can start in parallel with RF (which only had to wait for FR). (Common slip: assuming they conflict because PT later merges them — but the merge happens at PT, not before.)
Problem 2 — Research study
Set up. We are turning the description into a clean precedence table and answering questions about parallelism.
(i) LR(8, —), EA(10, —), DE(3, LR and EA), RP(7, EA), RT(12, DE and RP), AD(6, RT), WR(5, AD).
(ii) Start activities: LR and EA. Finish activity: WR.
(iii) Yes — LR and RP can run in parallel, but only once EA has finished. LR has no predecessor; RP needs EA. So LR could begin on day 0, while RP must wait 10 days for EA to finish before it can begin. They can overlap from day 10 onwards (since LR takes 8 days and may still finish first or might already be done by then). (More carefully: LR finishes at day 8, RP can only start at day 10 — so they do not actually overlap with these durations. A safer answer: structurally they can overlap because neither is in the other's predecessor chain.)
Problem 3 — Wedding planning
Set up. We are building the table and checking who can run in parallel after the venue is booked.
(i) SD(1, —), BV(2, SD), SI(3, BV), OF(2, BV), CC(2, BV), FC(1, SI and OF and CC).
(ii) Parallel set after BV: SI, OF and CC — each has BV as its only predecessor and none depends on the others.
(iii) The planner is breaking the rule that every activity must wait for ALL its immediate predecessors to finish. OF has BV as its only predecessor; starting OF before BV is signed would violate the precedence table and could mean ordering flowers for a venue that falls through. (One-sentence reason: precedence is a hard constraint, not a suggestion.)
Problem 4 — Software release
Set up. We are building the table, listing activities that depend only on SP, and naming the rule a junior dev is breaking.
(i) SP(5, —), UI(4, SP), BE(8, SP), FE(6, UI), IT(3, BE and FE), DC(2, SP), UA(2, IT and DC), RL(1, UA).
(ii) Activities with SP as the sole predecessor: UI, BE and DC. These three can all begin as soon as SP finishes (subject to having enough developers).
(iii) The claim breaks the rule that every activity must wait for its immediate predecessor(s) to finish. SP is listed as DC's predecessor, so DC cannot start until SP is finished. Correction: "DC has SP as a predecessor, so DC must wait for SP to finish — the table doesn't care whether the docs writer feels independent."
Problem 5 — School musical
Set up. We are building the table for the musical, identifying start/finish, and checking what happens when one row is moved.
(i) CS(1, —), AU(2, CS), CL(1, AU), RH(8, CL), BS(6, CS), MC(5, CL), TR(1, RH and BS and MC), ON(1, TR).
(ii) Start = CS. Finish = ON. Activities that can run in parallel with RH (once CL has finished): MC (shares predecessor CL with RH and is independent of RH). BS can also overlap with RH because BS only needs CS — by the time CL is done, BS may still be running or already done depending on dates.
(iii) If BS's predecessor changes from CS to CL, BS can no longer start until after auditions and the cast list (a 4-week delay: CS-AU-CL). It would no longer be parallel with AU or with the early part of RH planning. The new table is internally consistent (no cycles), but it does not match the original description, which only requires a script (CS) — not a cast — before building the set.