Decision Trees, Critical Path Analysis and Contribution
~55 min · WBS13 · 3.3.3
WBS13 · 3.3.3 · 55 min
Three techniques, one shared job: turning a decision that feels like a judgement call into numbers a business can actually check. A weighs an uncertain choice, finds the shortest a project can possibly take, and tells a firm whether one more unit — even at a strange price — adds to profit or not.
Key terms in this lesson
Before you read on
Two or three questions on exactly what this lesson teaches. Being wrong here is fine — it's the fastest way to find out what to pay attention to next.
Three techniques, one shared logic: deciding under real constraints
The three techniques in this lesson don't share a formula — they share a job. Each one takes a decision a manager could otherwise only argue about ('I think we should…') and turns it into something checkable: a handles a single choice made under genuine uncertainty (which option, given we don't know for sure what demand will be?); handles a multi-step project against a deadline (which activities actually control how long the whole thing takes?); and handles a recurring output or pricing decision (does one more unit — even at an unusual price — actually help or hurt profit?). None of the three removes the need for a manager's judgement entirely; each one narrows exactly where that judgement is still needed, which is the thread this lesson keeps coming back to.
Decision trees (3.3.3.3) are constructed left to right and solved right to left. A decision node, conventionally drawn as a small square, is a point where the firm itself chooses between mutually exclusive options — each option is its own branch, labelled with that option's cost. Every option branch leads to a chance node, conventionally a small circle, where an uncertain outcome — decided by the market or the wider world, not by the firm — branches out further, each outcome branch labelled with its probability (which must sum to 1 at that node, prequestion 1 above) and the payoff at the end of it. "Solving" the tree means working backward from the payoffs: calculate each chance node's , subtract that option's own cost to get its net gain, then choose the higher net gain and mark the rejected branch — usually with a double line or a cross through it — so the completed diagram itself shows both the working and the decision, not just the final answer.
This is a genuinely real WBS13 question, not a hypothetical: October 2024 Q2 (Publications Code WBS13_01_2410_MS, a 20-mark Evaluate) puts exactly this technique to Center Parcs, choosing between building a new holiday village (cost €520m; 0.8 probability of €780m success, 0.2 probability of a €120m loss) and taking over an existing one (cost €100m; 0.7 probability of €220m success, 0.3 probability of a €70m loss). The mark scheme's own worked answer: "(0.8 x €780) - (0.2 x €120m) - €520m = Expected Monetary Value €80m" for the new village, versus "(0.7 x €220m) - (0.3 x €70m) - €100m = Expected Monetary Value €33m" for the takeover — recommending the new village specifically because €80m beats €33m. Center Parcs' own formula nets the option's cost into the same expression as its weighted payoffs in one combined step; this lesson teaches the identical arithmetic as two named steps, EV then net gain, which lands on the same €80m and €33m once the failure branch is entered as a negative payoff — the diagram below shows exactly that, so the real figures and the two-step method can be checked against each other directly.
□ decision node · ○ chance node · two probability-weighted outcomes per option
- Build a new holiday village
- cost €520m
- Success — probability 0.8, payoff €780m
- Failure — probability 0.2, payoff −€120m
- Take over an existing village
- cost €100m rejected
- Success — probability 0.7, payoff €220m
- Failure — probability 0.3, payoff −€70m
Expected value €600m · Net gain €80m
Expected value €133m · Net gain €33m
Common error: Reading Extract F's 'Success 0.8, €780m' as the only figure that matters, and recommending the new village purely because €780m is Center Parcs' single largest possible payoff.
Correct: Weighting BOTH branches by their own probability, including the failure branch's own €120m loss, before comparing the two options' net gain (EMV) — €80m for the new village against €33m for the takeover. The mark scheme itself credits this exact caution: "even though the new village provided the highest potential return of €780m, Center Parcs may not base its decision on this alone as it would also consider the 20% probability of failure as well."
mark-scheme · Oct 2024 · Q2
Mechanism
Why expected value is a genuine weighted average, not just 'multiply and add'
Expected value looks like an arbitrary rule — multiply each payoff by its probability, add the results — until you ask what it's actually supposed to represent. Imagine the exact same 0.65-probability-of-high-demand, 0.35-probability-of-low-demand choice came up not once but many times over — say, across 1,000 genuinely independent product launches with identical odds. Roughly 650 of them would land the high-demand payoff and roughly 350 would land the low-demand payoff (that's what a 0.65 probability means: the long-run proportion of times the outcome occurs). The TOTAL payoff across all 1,000 launches would be approximately (650 × high payoff) + (350 × low payoff). Divide that total by 1,000 to get the AVERAGE payoff per launch, and the 650 and 350 turn back into 0.65 and 0.35: average payoff = (0.65 × high payoff) + (0.35 × low payoff) — exactly the expected-value formula. EV isn't an assumption bolted onto probability theory; it IS the long-run average payoff, derived directly from what a probability actually means. For a genuinely one-off decision — Thornfield Furniture Co., in the worked chain below, is choosing once, not running the same choice 1,000 times — EV is still the standard rational benchmark under the assumption that the firm is *risk-neutral*: indifferent between a certain amount and an uncertain gamble with the same average value. That assumption is exactly where the technique's real limitation lives, not in the arithmetic itself. Risk-neutrality claims a firm should feel no differently about a guaranteed £50,000 than about a coin-flip averaging out to the same £50,000 — but a real firm choosing between the two isn't choosing between equally attractive options: the coin-flip's bad outcome (say, £0) can mean a missed payroll or a broken supplier relationship that the guaranteed sum never risks at all, while its good outcome (say, £100,000) buys the same firm little it urgently needed that £50,000 alone didn't already cover. Treating every pound gained or lost as equally significant regardless of the firm's own position is precisely the assumption a genuinely risk-averse board has no reason to accept — which is the real content behind the spec's own decision-tree limitation (3.3.3.3c, 'ignores attitudes to risk'), stated here as a mechanism rather than left as a label. See the beyond-spec section below for the formal economic theory (diminishing marginal utility, loss aversion) this reasoning traces back to, and for what changes, numerically, once risk-neutrality is dropped.
Worked, in full
Solving the Thornfield Furniture Co. decision tree — right to left (VERIDIAN-original)
- 01
Thornfield Furniture Co. (VERIDIAN-original — built to demonstrate the same two-step EV-then-net-gain mechanism the real Center Parcs question above uses, but with cleaner round numbers for a first worked example; every figure here is invented for teaching purposes, not drawn from a real Pearson extract) is choosing between two ways to meet rising demand for its new sofa range. Option 1: build a factory extension, cost £480,000. Option 2: subcontract production to a partner manufacturer, cost £120,000. Both options face the identical demand uncertainty, from the same market research: probability of high demand = 0.65, probability of low demand = 0.35 (0.65 + 0.35 = 1.00 ✓, the construction rule from prequestion 1).
Earns: K (knowledge) — the decision correctly set up as two mutually exclusive options sharing one demand-uncertainty structure, not two unrelated calculations.
- 02
Factory extension's outcomes: high demand pays £1,100,000, low demand pays £350,000. Rolling back from the chance node: EV(factory) = (0.65 × £1,100,000) + (0.35 × £350,000) = £715,000 + £122,500 = £837,500.
Earns: An1 (application, first demonstration) — the probability-weighted-average mechanism derived above applied to specific stated figures, not the formula recited alone.
- 03
Subcontracting's outcomes: high demand pays £520,000, low demand pays £280,000. EV(subcontract) = (0.65 × £520,000) + (0.35 × £280,000) = £338,000 + £98,000 = £436,000.
Earns: An2 (application, second demonstration) — the same mechanism applied a second time, confirming it's a genuine method, not a one-off calculation trick that happened to work.
- 04
Neither £837,500 nor £436,000 is the figure that actually decides between the options — each option's own cost still has to be subtracted. Net gain(factory) = £837,500 − £480,000 = £357,500. Net gain(subcontract) = £436,000 − £120,000 = £316,000.
Earns: An3 (analysis) — net gain correctly identified as the real decision criterion, with the subtraction shown as a step rather than skipped.
- 05
£357,500 > £316,000, so Thornfield should build the factory extension — worth £41,500 more in expected net gain than subcontracting, despite costing £360,000 more upfront. The higher-cost option wins here specifically because its own outcomes are proportionally larger too, not because spending more is automatically better — a tree with a smaller gap between the options' outcomes could easily reverse this ranking, which is exactly why the comparison has to be recalculated for each new decision, never assumed from a previous one.
Earns: Eval (evaluation) — the result interpreted (why the costlier option won) with the specific-to-this-tree caveat stated explicitly, rather than generalised into a rule like 'invest more, get more.'
□ decision node · ○ chance node · two probability-weighted outcomes per option
- Build factory extension
- cost £480,000
- High demand — probability 0.65, payoff £1,100,000
- Low demand — probability 0.35, payoff £350,000
- Subcontract to a partner manufacturer
- cost £120,000 rejected
- High demand — probability 0.65, payoff £520,000
- Low demand — probability 0.35, payoff £280,000
Expected value £837,500 · Net gain £357,500
Expected value £436,000 · Net gain £316,000
Common error: Comparing the two options' raw expected values (£837,500 vs £436,000) and stopping there.
Correct: Subtracting each option's own cost from its EV first. Raw EV happens to rank the options the same way as net gain in THIS tree, but that's a coincidence of these particular numbers, not a guarantee — a diagram that never shows the cost subtraction step hasn't actually demonstrated the decision rule, only got lucky with it.
In your own words
In one sentence: why must a decision compare each option's NET gain (expected value minus its own cost), rather than comparing raw expected values, whenever the options being compared don't cost the same?
Critical path analysis: nature, purpose, and the vocabulary of a network
Critical path analysis (3.3.3.4a) exists to answer one question precisely: given a set of activities, some of which can only start once others finish, what is the minimum possible time the whole project can take, and which specific activities actually control that figure? A genuine 20/20 exemplar answer, quoted directly from the June 2022 examiner report on a Coca-Cola Zero Sugar relaunch question, states the purpose exactly: "Critical path analysis helps business plan out a timeline for a project and calculate the float time and find critical path so they can complete their project as soon as possible and meet their deadline." The real project in that question had a correct duration of 32 weeks, confirmed against the mark scheme — the underlying network data for that specific extract wasn't captured in this course's research pass, so the worked example below (Solmere Outdoors) is a fresh, VERIDIAN-original network built to demonstrate the identical mechanism at a smaller scale, not a reconstruction of the real Coca-Cola figures. A second real WBS13 question (Summer 2024 Q3, a 20-mark Evaluate on Burger King's restaurant-renovation programme) names two further genuine benefits worth stating precisely rather than folding into the purpose above. First, working through a network forces a careful, activity-by-activity assessment of what a project actually requires before work starts — the mark scheme credits this directly as reducing the project's own risk and cost, not merely as a side effect of finding the finish date. Second, once a network shows exactly when each activity is genuinely needed, deliveries can be scheduled just-in-time to arrive exactly then rather than sitting in storage beforehand — the mark scheme's own example is a restaurant's furniture and kitchen equipment — which keeps a firm's capital from being tied up in stock any earlier than the project actually needs it.
A network diagram is built from nodes (numbered circles marking a point in time — an event — when every activity leading into it has finished, and every activity leaving it can start) and activities (arrows connecting two nodes, each labelled with a letter and a duration). Two figures are written at every node: EST (earliest start time — the earliest point that node can genuinely be reached, found working forward from the start) and LFT (latest finish time — the latest point that node can be reached without pushing the whole project's finish date back, found working backward from the end). Total float is the spare time an individual activity carries; the critical path is the unbroken chain of zero-float activities running from the very first node to the very last — the derivation of exactly why zero float defines the critical path, rather than 'find the longest path' being an arbitrary rule, is the mechanism below.
CPA has genuine limitations too (3.3.3.4d), and the same June 2022 examiner report that quotes the 20/20 answer on CPA's usefulness above balances it directly against a quoted description of the technique's weaknesses: "critical path analysis is based on past data… External delays are extremely important in a project timeline and they are completely ignored in CPA. Additionally, CPA is expensive and time consuming." Unpacked, that's three separate limitations, not one: activity durations are usually estimated FROM how similar past activities took, so a genuinely new activity with no real precedent is a weaker input than the diagram's single neat number suggests; once a network is drawn, nothing in the diagram itself accounts for an unplanned EXTERNAL shock — a supplier failure, a strike, extreme weather — an activity's duration is treated as fixed unless a manager goes back and manually redraws the network around the disruption; and producing and keeping an accurate network current for a genuinely large real project is itself a real, ongoing cost in specialist planning time, not a free-to-produce add-on to running the project. Pearson's own Getting Started Guide names a distinct fourth limitation under the same 'assumptions and estimates' heading: whether "the next activity can actually start on time" — the network's own built-in assumption that a successor activity begins the instant its predecessor's node is reached, with no handover delay, inspection, sign-off, or delivery wait modelled anywhere in the diagram. A network can have every individual activity duration estimated correctly and still run late in practice, purely because this zero-lag assumption between activities doesn't hold — a limitation about the STRUCTURE of the technique itself, not about any one number being wrong. The Burger King mark scheme (Summer 2024 Q3, above) confirms a fifth, genuinely distinct limitation worth separating from all four above: a single completed network — however accurately its own durations are estimated — describes ONE project, not a template guaranteed to hold everywhere a firm rolls the identical programme out. Its own words: "the CPA may not be effective for all restaurants as they may have different layouts and building requirements. The availability of local contractors to undertake the renovations will be different in different locations." A network built from genuinely accurate data for restaurant #1 can still mislead at restaurant #47, because the underlying conditions the estimate depended on — site layout, local contractor availability — are different THERE, not merely more uncertain.
Why a delay on one activity can vanish completely while an identical delay on another sinks the whole project
In plain terms
A tiny building project has just three jobs. Ordering materials takes 3 weeks and can start straight away. Getting planning permission takes 6 weeks and can also start straight away, at the same time — the two jobs run side by side, nobody waiting on anybody yet. Actual construction can only begin once BOTH the materials have arrived AND permission has come through, and it then takes 2 weeks. Materials are ready by week 3, but permission isn't ready until week 6 — so construction has to wait for the slower of the two, and starts at week 6, finishing at week 8. Eight weeks, start to finish, is the fastest this project can possibly go. Now ask: what happens if permission is delayed by just 1 week, taking 7 weeks instead of 6? Materials are still sitting there, ready since week 3 — but construction still can't start until permission actually arrives, which is now week 7. Construction still takes its 2 weeks, so the whole project now finishes at week 9 — one week later than planned. The 1-week delay on permission became a full 1-week delay on the entire project; nothing absorbed it. Compare that to delaying the MATERIALS instead. Say ordering materials is mismanaged and takes 6 weeks instead of 3 — double the time it was meant to take, a 3-week delay. Materials now arrive at week 6 — but that's exactly when permission was arriving anyway, so construction still starts at week 6, right on the original schedule, and still finishes at week 8. A 3-week delay on materials cost the project nothing at all, because materials were never the thing everyone else was actually waiting on. There's a limit to that free ride, though. Delay materials by 4 weeks instead of 3 — 7 weeks total — and materials now arrive at week 7, a week AFTER permission (which still finishes on time at week 6). Now materials is the one holding construction up: it can't start until week 7, and the project finishes at week 9, a week late. The first 3 weeks of the materials delay cost nothing — they were just catching up to permission's own week-6 finish — but the 4th week leaked straight through to the finish date, because by then materials had become the slower of the two jobs. So the same activity can be either 'free to delay' or 'the whole project's deadline,' depending purely on whether anything else in the project is already taking at least as long. Permission had zero weeks of slack from the very start — it was always the slower of the two parallel jobs, so any delay to it is a delay to everything after it. Materials had exactly 3 weeks of slack — the gap between how long it actually takes (3 weeks) and how long it's allowed to take before it starts costing the project anything (6 weeks) — and that 3-week cushion, not some vaguer sense of 'materials matters less,' is precisely why the first 3 weeks of its delay vanished and the 4th didn't.
The three numbers just tracked all have formal names in network analysis. The earliest a job can genuinely start is its EST (earliest start time) — for construction, that meant taking the LATER of materials' finish (week 3) and permission's finish (week 6), i.e. week 6, because a job that depends on two things can't start until BOTH are actually ready. The latest a job can be allowed to finish without pushing the project's own finish date back is its LFT (latest finish time) — for permission, that was week 6 exactly, since construction needs it by then; for materials, that was ALSO week 6, for the identical reason — construction doesn't care which of the two arrives first, only that both have arrived by week 6. The gap between when a job is actually ready (its own earliest finish) and when it's allowed to be ready (its LFT) is its total float: permission's float was 6 − 6 = 0 weeks; materials' float was 6 − 3 = 3 weeks — exactly the cushion that absorbed the first 3 weeks of delay and no more. A job with zero float, like permission, sits on what's called the critical path — the chain of jobs with no spare time anywhere along it, where delaying any single link delays the finish date by the identical amount.
Formally
For any activity, total float = LFT(the node it finishes at) − EST(the node it starts from) − its own duration. EST is built forward through the network, node by node, taking the LATER of any routes converging on a node (construction's EST = max(3, 6) = 6 above); LFT is built backward from the project's finish date, taking the EARLIER of any routes a node feeds into. The critical path is the unbroken chain of activities whose total float is exactly zero, running from the project's first node to its last — permission→construction in the toy example above, A→B→D→F in the full Solmere Outdoors network below. Delaying any activity on that chain delays the finish date by the same amount; delaying an activity off it, by up to its own float, changes nothing. The mechanism below proves this holds for a network of any size, not just a three-activity toy case, by tracking exactly what an LFT value is allowed to mean once it's been defined.
Mechanism
Why the critical path is exactly the path with zero total float
Total float of an activity is defined as LFT(the node it ends at) minus EST(the node it starts from) minus its own duration — the amount of genuine slack available to it. If that number is positive, the activity can start up to that many weeks late, or run that many weeks over, and the node it feeds into is STILL reached by that node's own LFT — because LFT already encodes the latest the rest of the network can tolerate reaching that point while the whole project still finishes on schedule. Now consider an activity whose float is exactly zero. There is no slack: the node it starts from is only reached at its own EST at the earliest, the node it ends at must be reached by its own LFT at the latest, and the activity's duration exactly uses up the entire gap between the two — there is no room left over. Delay that activity by even one day, and the node it feeds into is necessarily reached one day later than its LFT. But LFT was defined, by the backward pass, as the latest that node can be reached without delaying the FOLLOWING node past its own LFT — so that next node is now late too, by the same argument, and the one after it, all the way to the project's final node. A single zero-float activity running late cascades, node by node, into the project itself finishing late, by exactly the amount of the original delay. The critical path is simply the name for the unbroken chain of activities where this zero-slack condition holds start to finish — and because delaying ANY link in that chain delays the whole project, by the cascade just derived, "critical path = longest path through the network" isn't a separate rule to memorise. It's the same fact stated a different way: the longest route through the network is, by definition, the one route with no spare time to lose, because every other route is shorter and therefore has slack relative to it.
Worked, in full
Deriving EST, LFT and total float for Solmere Outdoors' tent launch (VERIDIAN-original)
- 01
Six activities take Solmere Outdoors from market research to launch. A: Market research, 3 weeks, no predecessor. B: Product design, 4 weeks, after A. C: Packaging design, 2 weeks, after A. D: Prototype build, 5 weeks, after B. E: Regulatory paperwork, 3 weeks, after C. F: Launch marketing campaign, 4 weeks, after both D and E. Drawn as a network: node 1 (start) →A→ node 2; from node 2, B and C run in parallel to nodes 3 and 4; D (from node 3) and E (from node 4) both converge on node 5, so F cannot start until both are finished; F runs from node 5 to node 6 (finish).
Earns: K (knowledge) — the precedence list translated into a genuine network structure, with the two structural features that make it interesting — node 2 splitting into two parallel branches, node 5 merging them back — stated explicitly.
- 02
Forward pass: EST at each node is the EARLIEST it can possibly be reached, found by taking the slower of any routes converging on it. EST(1)=0. EST(2)=EST(1)+3=3. EST(3)=EST(2)+4=7. EST(4)=EST(2)+2=5. EST(5) is the genuinely interesting one, since both D and E lead into it: EST(5)=max(EST(3)+5, EST(4)+3)=max(12, 8)=12. EST(6)=EST(5)+4=16. The project cannot finish before week 16, however efficiently everything else runs, because node 5 genuinely cannot be reached before week 12 — the route through D is the slower of the two.
Earns: An1 (analysis, first move) — the max() rule at a converging node derived from what 'earliest possible' actually requires (waiting for the slower route in), not applied as a memorised step.
- 03
Backward pass: LFT at each node is the LATEST it can be reached without pushing the week-16 finish date back, found working from the end. LFT(6)=16 (the project's own finish date). LFT(5)=16−4=12. LFT(4)=12−3=9. LFT(3)=12−5=7. LFT(2) is the symmetric interesting case, since both B and C leave from it and must each satisfy their own downstream deadline: LFT(2)=min(LFT(3)−4, LFT(4)−2)=min(3, 7)=3 — the TIGHTER of the two, since node 2 has to be ready in time for whichever route is less forgiving. LFT(1)=3−3=0.
Earns: An2 (analysis, second move) — the min() rule at a diverging node derived symmetrically to the max() rule above: a node feeding two later deadlines has to satisfy whichever is tighter.
- 04
Total float = LFT(end node) − EST(start node) − duration. Float(A)=LFT(2)−EST(1)−3=3−0−3=0. Float(B)=LFT(3)−EST(2)−4=7−3−4=0. Float(D)=LFT(5)−EST(3)−5=12−7−5=0. Float(F)=LFT(6)−EST(5)−4=16−12−4=0. Four activities, zero float each — a chain with no slack anywhere along it.
Earns: An3 (analysis, third move) — float computed explicitly for every activity that turns out to be critical, not asserted by eyeballing the diagram.
- 05
Float(C)=LFT(4)−EST(2)−2=9−3−2=4. Float(E)=LFT(5)−EST(4)−3=12−5−3=4. Both positive: C and E can each run up to 4 weeks over, or start up to 4 weeks late, without moving node 6's week-16 finish date. Check this independently: the alternative route A→C→E→F takes 3+2+3+4=12 weeks — four weeks short of the 16-week critical route A→B→D→F, exactly matching the float figure, because 'how much shorter is this route than the longest one' and 'how much float its activities carry' are the same fact, arrived at two different ways.
Earns: An4 (analysis, fourth move) — the float figures for the non-critical activities cross-checked against an independently-derived route length, not left as an unverified formula output.
- 06
The critical path is A→B→D→F (3+4+5+4=16 weeks, matching the project duration exactly). Delay A, B, D or F by even a week and the finish date moves by the same week — the cascade derived in the mechanism above. C and E can each absorb up to 4 weeks of delay with zero effect on the launch date, which is precisely why time spent accelerating packaging design (C) or chasing regulatory paperwork (E) faster than necessary buys Solmere Outdoors nothing at all — see the chain-drill below.
Earns: Eval (evaluation) — the critical-path definition (zero float, unbroken, start to finish) explicitly reconciled with the popular 'find the longest path' shortcut, rather than left as two unconnected facts.
Source — Examiner report, June 2022
"Critical path analysis helps business plan out a timeline for a project and calculate the float time and find critical path so they can complete their project as soon as possible and meet their deadline."
Critical path: 1 → 2 → 3 → 5 → 6 · 16 total
- 1
- EST 0 · LFT 0 · on the critical path
- 2
- EST 3 · LFT 3 · on the critical path
- 3
- EST 7 · LFT 7 · on the critical path
- 4
- EST 5 · LFT 9
- 5
- EST 12 · LFT 12 · on the critical path
- 6
- EST 16 · LFT 16 · on the critical path
- 1 → 2
- Market research — 3, on the critical path
- 2 → 3
- Product design — 4, on the critical path
- 2 → 4
- Packaging design — 2
- 3 → 5
- Prototype build — 5, on the critical path
- 4 → 5
- Regulatory paperwork — 3
- 5 → 6
- Launch marketing campaign — 4, on the critical path
Common error: Writing only one figure in each node, or writing EST and LFT the wrong way round (LFT on top, EST on the bottom).
Correct: Two figures per node, always — EST top, LFT bottom — with total float then calculated per ACTIVITY (LFT of the node it points into, minus EST of the node it starts from, minus its own duration), not read directly off the node figures themselves.
What the exam actually asks for is completing a network, not building one from a blank page. Pearson's own Getting Started Guide for this qualification states students are "not required to construct critical path diagrams from scratch" — the standard task is completing a semi-complete network (some nodes, activities, or EST/LFT figures already given) and then interpreting it, specifically for "what this shows a business in terms of its resource management" (the guide's own framing), not as a bare arithmetic exercise. EST and LFT calculations are tested both as fill-in-the-gaps on a semi-complete diagram and as read-and-use on one that's already finished. The full Solmere Outdoors network above, built from a written precedence list, is deliberately the harder version of this exercise: understanding how to build a network from nothing is what makes finishing someone else's half-built one straightforward, not the other way round.
Complete it yourself
Complete the chain — why activity C's float doesn't help Solmere Outdoors launch any sooner
- 01
Activity C (Packaging design) starts at node 2, which is reached at EST=3 at the earliest, and C takes 2 weeks — so C finishes, at the earliest, in week 5.
- 02
Activity E (Regulatory paperwork, which needs C finished first) can therefore start no earlier than week 5 — but node 5, which both D and E feed into, doesn't actually need E to be ready until week 12, because D alone (the other route into node 5) already takes until week 12 to finish.
In your own words
In one sentence: why would shortening activity D (Prototype build) by 2 weeks pull the project's finish date forward by 2 weeks, while shortening activity E (Regulatory paperwork) by 2 weeks would not change the finish date at all?
Contribution: what it measures, and why it's a decision tool, not just a number
per unit — selling price minus variable cost per unit — was already defined for break-even analysis; total contribution (contribution per unit × units sold) is the same idea scaled up. A genuine, verified worked example: Lush's bath-soap range sold at £5.50 per unit with variable cost of £1.00 per unit gives contribution per unit of £5.50 − £1.00 = £4.50; on 3,300,000 units sold in a month, total contribution = £4.50 × 3,300,000 = £14,850,000 — confirmed directly from the June 2023 examiner report, which quotes two independently valid working methods for reaching this exact figure (per-unit contribution × units, and total revenue minus total variable cost) in a genuine full-marks exemplar script.
The spec's third contribution sub-point (3.3.3.5c) — using contribution 'as a decision-making technique' — is where this idea earns its place in this lesson rather than the break-even one, and it feeds three genuinely distinct real business decisions. First, accept/reject a one-off order priced below normal selling price: worked in full below, using contribution rather than the normal price or full average cost as the test. Second, whether to discontinue a product: a product with POSITIVE contribution is still adding to overall profit even if it isn't covering its full 'fair share' of allocated fixed overhead under an absorption-costing approach — dropping it would remove that positive contribution and, because most fixed costs don't actually disappear when one product line does, could make the firm's TOTAL profit worse, not better. Only a product with genuinely NEGATIVE contribution (price below variable cost) is a candidate for discontinuation on cost grounds alone. Third, ranking products when a scarce resource limits output — machine hours, skilled labour hours, or a scarce raw material — where the correct ranking is contribution PER UNIT OF THE SCARCE RESOURCE, not contribution per unit of output and not total profit; a product with a lower contribution per unit can still be the better use of a genuinely limited resource if it uses far less of that resource per unit than a higher-contribution alternative does.
Mechanism
Why contribution, not full unit cost, is what actually drives a short-run accept/reject decision
This is the same cancellation this course's WEC13 Profits and Losses lesson derives algebraically for the shutdown decision — the mechanism transfers exactly, just applied to a different business question. A firm comparing 'accept this order' against 'reject it' is comparing two possible profit outcomes. Accept: profit = (profit from existing business, unaffected) + (order's own revenue) − (order's own variable cost) − (any EXTRA fixed cost the order specifically causes). Reject: profit = (profit from existing business, unaffected) + 0. Subtract the second from the first: the difference is exactly (order's revenue − order's variable cost) − (extra fixed cost caused) — order's contribution, minus whatever new fixed cost the order genuinely triggers. The existing-business profit term cancelled out of that subtraction completely, and so did every fixed cost the firm is committed to paying regardless of which option is chosen — which is the general 'sunk cost' principle, derived rather than merely asserted: a cost that is identical under every option being compared carries zero weight in choosing between them, because it appears on both sides of the subtraction and cancels exactly, leaving only the costs and revenues that genuinely differ between accepting and rejecting to determine the answer. Whenever the order uses only SPARE capacity — machine time, staff hours, or floor space the firm was already paying for and not otherwise using — the extra-fixed-cost term is zero by definition, because nothing new had to be bought or hired to fulfil it. What's left is simply: accepting is worthwhile exactly when the order's own contribution is positive. Full average cost, by contrast, already has a share of the SAME existing fixed costs baked into it — costs the order didn't cause and wouldn't be avoided by rejecting it. Comparing an order's price to average cost silently double-counts that fixed-cost share against a decision the fixed cost has nothing to do with, which is exactly the trap the worked chain below and its multi-mark MCQ are built to test.
Worked, in full
Should Aldergate Print Co. accept the wholesale order? — deriving the rule, not asserting it (VERIDIAN-original)
- 01
Aldergate Print Co. normally sells posters at £8.00 each; variable cost per poster (paper, ink, packaging) is £3.00, so normal contribution per poster = £8.00 − £3.00 = £5.00. This month it has genuine spare capacity: 5,000 posters could be produced above its existing order book without hiring extra staff or extending machine hours.
Earns: K (knowledge) — the spec's own contribution definition applied to stated figures, with 'spare capacity' established as a fact of the scenario rather than assumed.
- 02
A wholesale buyer offers a one-off order for exactly those 5,000 posters, at £4.50 each, with no ongoing commitment beyond this month. Special-order contribution per poster = £4.50 − £3.00 = £1.50 — still positive, even though it's well below the normal £5.00 figure. The two contribution figures are answering different questions and aren't meant to match.
Earns: An1 (application, first demonstration) — contribution recalculated at the special order's own price, not assumed to inherit the normal £5.00 figure.
- 03
Aldergate's total fixed costs (rent, salaried staff, equipment) are already fully committed for this month regardless of whether the order is accepted — they don't rise by a single pound if it goes ahead, because it uses capacity that would otherwise sit idle. By the mechanism derived above, the only thing that genuinely differs between 'accept' and 'reject' is the order's own contribution, not Aldergate's average or full cost per poster.
Earns: An2 (analysis) — the mechanism (fixed cost is identical either way) stated as the reason contribution, not average cost, is the correct comparison here — not asserted as a bare rule.
- 04
Extra profit from accepting = special-order contribution per poster × units = £1.50 × 5,000 = £7,500, added directly to Aldergate's profit for the month. Rejecting the order doesn't save a single pound of fixed cost — it simply leaves £7,500 of achievable extra profit unclaimed.
Earns: An3 (analysis) — the total figure computed and its meaning stated (added profit, not an avoided cost), closing the argument rather than stopping at the per-unit figure.
- 05
The naive alternative — comparing £4.50 to the £8.00 normal price, or to an average total cost that includes a share of fixed costs this order didn't cause — would wrongly recommend rejecting a genuinely profit-increasing order. A positive-contribution order priced below what full-cost thinking would demand is not automatically a loss-making order, and telling the two apart is precisely what 3.3.3.5c tests.
Earns: Eval (evaluation) — the correct rule set directly against the specific wrong rule it's easy to reach for, with the trade-off named explicitly rather than left implicit.
Source — Examiner report, June 2023
"£5.50 − £1.00 = £4.50 per unit; £4.50 × 3,300,000 = £14,850,000"
In your own words
In one sentence: why does the special-order decision above depend entirely on whether spare capacity genuinely exists, and not just on whether the special-order price exceeds variable cost?
Named traps
- workings-earn-marks-even-with-a-wrong-final-answer
- Confirmed as a paper-wide pattern in this facts bank — repeated as explicit advice in the October 2022, June 2022 and June 2023 examiner reports: "Marks can still be awarded even with an incorrect answer" if workings and the correct method are shown. This applies directly to every calculation in this lesson: show every EST/LFT figure at every node, not just the final float number; show the EV-then-net-gain steps separately in a decision tree, not a single unexplained final figure; show contribution per unit before multiplying by units sold. A wrong final answer with the right method visible can still score most of the available marks — a right final answer with no visible working often cannot, on this paper's own confirmed marking pattern.
- full-cost-fallacy-on-a-short-run-decision
- Not confirmed against a specific WBS13 extract for this exact sub-topic (the facts bank found no primary-source contribution-decision-making example beyond the Lush contribution calculation itself), but this is the single most common real error in applying 3.3.3.5c: comparing a special-order or below-normal price to average TOTAL cost (which includes an allocated share of fixed costs the order didn't cause) rather than to variable cost alone. The mechanism above shows exactly why this double-counts a cost that's irrelevant to the decision — treat 'the price doesn't cover its share of overheads' as a warning sign that full-cost thinking has crept into what should be a contribution-only comparison.
- float-is-per-activity-not-a-shared-pool
- This specific framing (float as a per-activity figure, not a shared branch-wide pool) is not itself confirmed against a real WBS13 extract — neither of the two genuine CPA facts this lesson now has (the 32-week Coca-Cola duration; the Burger King Activity C = 1 week float, Summer 2024 Q3) states it this way — so it's flagged here as a genuine, mechanism-derived caution rather than a quoted mark-scheme point. Total float belongs to the specific activity it's calculated for, not to the whole non-critical branch as a shared allowance. In the Solmere Outdoors network above, activities C and E each individually carry 4 weeks of float — but that is NOT 8 weeks of combined slack available somewhere on that branch; delaying C by 4 weeks already uses up all of the branch's slack, leaving E with zero genuine room left even though its own float figure, recalculated in isolation, still reads as 4.
- one-network-doesnt-generalise-across-every-site
- Confirmed directly in the real Summer 2024 WBS13 mark scheme (Q3, Burger King's multi-restaurant renovation programme, 20-mark Evaluate): "the CPA may not be effective for all restaurants as they may have different layouts and building requirements. The availability of local contractors to undertake the renovations will be different in different locations." This is a genuinely different limitation from the past-data-estimate point taught above (CPA teach block, limitations paragraph) — that one is about an estimate being WRONG; this one is about an estimate being RIGHT for the project it was built from and still not transferring cleanly to the next one. A firm rolling the identical renovation programme out across many sites cannot treat one site's completed network as a template for the rest — each site's own layout and contractor availability has to be assessed on its own terms, not inherited from a previous network that happened to be accurate elsewhere.
- raw-expected-value-instead-of-net-gain
- The real Oct 2024 Center Parcs mark scheme (above) confirms decision trees as a topic now have a genuine WBS13 anchor — but its own worked answer computes cost-netted EMV as one combined step and never isolates a bare, un-netted expected-value figure the way this course's own two-step method does, so this SPECIFIC error (stopping at raw EV, not yet subtracting cost) remains unconfirmed against a primary-source WBS13 extract. It is still the single most consequential mechanical error the worked chain above is built to prevent: stopping at each option's expected value and comparing those figures directly, without subtracting each option's own cost. Whenever two options being compared have different costs — which is the normal case, not the exception — comparing raw EV can rank the options differently from comparing net gain, exactly as the Option P vs Option Q diagram above demonstrates. Always subtract cost from EV before comparing.
The conditional move
Complete: "Shortening a project's overall completion time by speeding up one activity only works if ___."
Complete: "Accepting a one-off order priced below a product's normal selling price increases profit only if ___."
Beyond the spec
The mechanism above already explains WHY a risk-averse board can rationally reject a decision tree's own net-gain recommendation — the spec's decision-tree 'limitations' point (3.3.3.3c, 'ignores attitudes to risk') is core, examinable content, not enrichment, so that reasoning lives in the mechanism block itself, not only here. What genuinely IS beyond spec is the formal economic machinery behind it: the named theory and theorists that turn 'risk attitudes matter' from an intuitive argument into a citable, rigorously-derived one — useful for a student who wants to write 'this is a well-established idea in economics, not just my opinion' rather than merely gesturing at the intuition a second time.
Expected value assumes a firm is risk-neutral — indifferent between a certain amount and an uncertain gamble with the identical average value. Daniel Bernoulli's 1738 resolution of the St Petersburg paradox was the first formal argument that this assumption often fails: he proposed that decision-makers actually maximise expected UTILITY, not expected monetary value, and that utility rises more slowly than money itself — a form of diminishing marginal utility of wealth. A guaranteed £50,000 is worth MORE to most real decision-makers than a 50% chance of £100,000 and a 50% chance of £0, even though both have an identical £50,000 expected value, because the extra utility from the second £50,000 is smaller than the utility already gained from the first. A risk-averse board facing the Thornfield Furniture Co. tree above might reject the higher-net-gain factory-extension option specifically because its own outcomes are more spread out (£1,100,000 or £350,000) than subcontracting's narrower range (£520,000 or £280,000), even with a lower expected net gain — a genuinely rational choice once the board's aversion to variance, not just its average, is taken into account. Daniel Kahneman and Amos Tversky's 1979 prospect theory goes further still, with experimental evidence that real decision-makers weight losses roughly twice as heavily as equivalent-sized gains (loss aversion) — which is precisely why 'decision trees ignore attitudes to risk' is a substantive, well-founded limitation of the technique, not a throwaway line to state and move past.
Retrieval — with feedback on every choice
Which of the following correctly distinguishes a decision node from a chance node in a decision tree?
Option P costs £200,000 to set up; it has a 0.5 probability of paying £500,000 and a 0.5 probability of paying £100,000. Option Q costs £30,000 to set up; it has a 0.5 probability of paying £250,000 and a 0.5 probability of paying £90,000. (VERIDIAN-original.)
Based on net gain, which option should be chosen, and why?
□ decision node · ○ chance node · two probability-weighted outcomes per option
- Option P
- cost £200,000 rejected
- Higher payoff — probability 0.5, payoff £500,000
- Lower payoff — probability 0.5, payoff £100,000
- Option Q
- cost £30,000
- Higher payoff — probability 0.5, payoff £250,000
- Lower payoff — probability 0.5, payoff £90,000
Expected value £300,000 · Net gain £100,000
Expected value £170,000 · Net gain £140,000
Common error: Picking Option P because its raw expected value (£300,000) is higher than Option Q's (£170,000), and stopping there.
Correct: Subtracting each option's own cost before comparing: net gain(P) = £300,000 − £200,000 = £100,000; net gain(Q) = £170,000 − £30,000 = £140,000. Q wins on net gain despite losing on raw EV — the reverse of the Thornfield tree above, and exactly why the two figures can never be assumed to agree.
Retrieval — with feedback on every choice
In the Solmere Outdoors network above, which one of the following activities has a positive total float?
Which of the following is a genuine limitation of critical path analysis, confirmed directly in a real examiner report?
Aldergate Print Co. normally sells posters at £8.00 each; variable cost per poster is £3.00. This month the firm has genuine spare capacity to produce 5,000 more posters without affecting its existing order book. A wholesale buyer offers a one-off order for exactly 5,000 posters at £4.50 each, with no ongoing commitment beyond this month. (VERIDIAN-original, testing the exact reasoning structure the real spec point 3.3.3.5c examines.)
Using contribution, which of the following correctly evaluates whether Aldergate Print Co. should accept the wholesale buyer's order?
Lush's bath-soap range sells at £5.50 per unit; variable cost is £1.00 per unit. On 3,300,000 units sold in a month, what is total contribution?
Same question, every level
Evaluate the extent to which quantitative decision-making techniques remove the need for managerial judgement when a business must choose between different ways of expanding output. (VERIDIAN-original question, written in the style confirmed across multiple WBS13 series — not a reproduction of any single past-paper question.)
20 marks available
Decision trees show probabilities and costs, and critical path analysis shows how long a project takes. These techniques give the business numbers to help them decide, so they are useful for making better decisions.
Isolated, recall-level statements about what each technique 'shows', with no named business, no worked mechanism, and no diagram. The closing sentence is a generic assertion, not an argument — matches the verified L1 (1-4) descriptor: weak or no relevant application, argument fails to connect causes and consequences.
- Decision tree: EV = Σ(probability × payoff) at each chance node. Compare NET gain (EV − cost), never raw EV.
- CPA: EST = forward pass. LFT = backward pass. Total float = LFT(end node) − EST(start node) − duration.
- Critical path = the unbroken zero-float chain, start to finish — delaying any activity on it delays the whole project.
- Contribution = price − variable cost per unit. Accept a below-price order only if contribution is positive AND spare capacity exists.
- Never conclude a technique removes judgement — probabilities, durations and costs are all estimates someone still had to make.
Not affiliated with or endorsed by Pearson Edexcel. Every quotation and figure attributed to a mark scheme or examiner report in this lesson was independently verified against the primary Pearson document, not carried over from prior course material. This paper (WBS13) had no local source archive anywhere on the machine: every source behind it was fetched fresh, directly from qualifications.pearson.com. Decision trees now have one confirmed real primary-source example — October 2024 Q2 (Publications Code WBS13_01_2410_MS), Center Parcs choosing between building a new holiday village and taking over an existing one, with genuine EMV figures of €80m and €33m — found on a ninth series after two earlier passes (the original 6, then 8 as of 2026-08-28) checked and found none. The Thornfield Furniture Co. and Option P/Option Q examples in this lesson stay VERIDIAN-original and labelled as such: Center Parcs' own hand-drawn tree in Extract F wasn't machine-reproducible from the question paper's image, so only its numbers and indicative-content prose were captured, not a second full diagram-plus-working chain. Critical path analysis has two confirmed real facts (a 32-week Coca-Cola Zero Sugar project, June 2022; and Burger King's 11-week restaurant renovation, Activity C at 1 week of float, Summer 2024 Q3) without the underlying network data for either, so the worked CPA network here is also VERIDIAN-original — but the two benefits and the multi-site limitation drawn from the Burger King mark scheme's own indicative content are genuine, sourced teaching, not invented. Contribution's Lush figures (£4.50 per unit, £14,850,000 total) are genuine, verbatim-checked mark-scheme content.
Which of the following correctly distinguishes a decision node from a chance node in a decision tree?
- AA decision node is drawn as a circle; a chance node is drawn as a square
This reverses the standard convention — a decision node is the square (the firm's own choice), a chance node is the circle (an uncertain, externally-decided outcome).
- BA decision node shows costs; a chance node shows probabilities — there is no other difference between them
Costs and probabilities are what get WRITTEN on the branches at each type of node, but that's a surface feature, not the actual distinction. The real difference is who or what determines the branch: the firm at a decision node, external uncertainty at a chance node.
- A decision node is a point where the firm itself chooses between options; a chance node is a point where an uncertain outcome, decided by the market rather than the firm, branches out
Correct. This is the actual distinction the diagram is built on: control. The firm controls what happens at a decision node (which option to pick); it does not control what happens at a chance node (which way demand, or any other external factor, turns out).
- DDecision nodes and chance nodes are interchangeable terms for the same structure
They represent genuinely different things — one is a choice the firm makes, the other is an outcome the firm has no control over. Treating them as interchangeable would make it impossible to correctly construct or interpret a tree at all.
Traps tested: Reverses standard shapes · Surface feature not mechanism · Collapses a real distinction
Option P costs £200,000 to set up; it has a 0.5 probability of paying £500,000 and a 0.5 probability of paying £100,000. Option Q costs £30,000 to set up; it has a 0.5 probability of paying £250,000 and a 0.5 probability of paying £90,000. (VERIDIAN-original.)
Based on net gain, which option should be chosen, and why?
- Option Q — its net gain (£140,000) exceeds Option P's (£100,000), even though Option P has the higher raw expected value (£300,000 vs £170,000)
Correct. EV(P) = 0.5×£500,000 + 0.5×£100,000 = £300,000; net gain(P) = £300,000 − £200,000 = £100,000. EV(Q) = 0.5×£250,000 + 0.5×£90,000 = £170,000; net gain(Q) = £170,000 − £30,000 = £140,000. Q wins on the figure that actually matters, despite losing on raw EV.
- BOption P — it has the higher expected value, and expected value is what a decision tree is built to compare
A decision tree compares expected value at the CHANCE NODE stage, then subtracts cost to reach the actual decision criterion, net gain. Stopping at raw EV — as this choice does — is exactly the trap this whole comparison is designed to expose.
- COption Q — it is cheaper to set up, and a cheaper option is always the safer choice
Being cheaper isn't itself the decision rule — Q happens to also win on net gain here, but that's because its EV didn't fall by as much as its cost saving, not because 'cheaper' is a rule on its own. A cheaper option with a low enough EV could easily lose on net gain instead.
- DIt is a tie — both options have the same expected net gain once rounded
£100,000 and £140,000 are not close, let alone equal — check the arithmetic (0.5×500,000+0.5×100,000=300,000, minus 200,000=100,000; 0.5×250,000+0.5×90,000=170,000, minus 30,000=140,000) rather than estimating.
Traps tested: Raw ev instead of net gain · Cost alone not net gain · Arithmetic slip
In the Solmere Outdoors network above, which one of the following activities has a positive total float?
- AActivity A (Market research)
Float(A) = LFT(2)−EST(1)−3 = 3−0−3 = 0 — A is on the critical path, not carrying float.
- BActivity D (Prototype build)
Float(D) = LFT(5)−EST(3)−5 = 12−7−5 = 0 — D is on the critical path.
- Activity C (Packaging design)
Correct. Float(C) = LFT(4)−EST(2)−2 = 9−3−2 = 4 weeks — C is the non-critical activity that can run up to 4 weeks over without delaying the project.
- DActivity F (Launch marketing campaign)
Float(F) = LFT(6)−EST(5)−4 = 16−12−4 = 0 — F is on the critical path, the very last link in it.
Traps tested: Misidentifies critical activity as floating
Which of the following is a genuine limitation of critical path analysis, confirmed directly in a real examiner report?
- AIt cannot be used on any project with more than about ten activities
No such limit exists — CPA's mechanism (forward pass, backward pass, float) works identically regardless of network size; large real projects use it routinely. This invents a constraint the technique doesn't actually have.
- It ignores external delays once the network is drawn, and its activity durations are typically estimated from past data that may not hold for a genuinely new activity
Correct — confirmed directly in the June 2022 examiner report: CPA "is based on past data" and "external delays… are completely ignored." A supplier failure or a genuinely unprecedented activity are exactly the cases where the diagram's neat single-figure durations are weakest.
- CIt always produces an inaccurate project duration, even when every activity duration turns out to be estimated correctly
This overclaims — if every duration estimate genuinely holds and no external delay occurs, the forward/backward pass gives an exactly correct duration; that's the whole mechanism derived earlier in this lesson. The real limitation is about the INPUTS (estimates, no room for shocks), not a flaw in the arithmetic itself.
- DIt cannot show which activities have spare time, only the length of the critical path
The opposite is true — total float, calculated per activity, is precisely how CPA shows spare time on every non-critical activity (C and E in the Solmere Outdoors network above, for instance). This misdescribes what the technique actually outputs.
Traps tested: Invents a limitation · Overclaims the limitation · Misunderstands technique output
Aldergate Print Co. normally sells posters at £8.00 each; variable cost per poster is £3.00. This month the firm has genuine spare capacity to produce 5,000 more posters without affecting its existing order book. A wholesale buyer offers a one-off order for exactly 5,000 posters at £4.50 each, with no ongoing commitment beyond this month. (VERIDIAN-original, testing the exact reasoning structure the real spec point 3.3.3.5c examines.)
Using contribution, which of the following correctly evaluates whether Aldergate Print Co. should accept the wholesale buyer's order?
- AReject — because £4.50 is well below Aldergate's normal £8.00 selling price, accepting it would reduce the firm's average revenue per poster and therefore its profit
This compares the special-order price to the NORMAL price, not to variable cost — the wrong benchmark for a spare-capacity decision. A below-normal price can still be profit-increasing, which is exactly what this answer misses.
- Accept — the special-order price of £4.50 still exceeds the £3.00 variable cost per poster, giving a positive contribution of £1.50 per unit; because the order uses spare capacity, existing fixed costs are unaffected either way, so this £1.50 per poster (£7,500 across the order) adds directly to profit
Correct, and this is the fully-integrated version: it names the correct benchmark (variable cost, not price or full cost), confirms the contribution is positive, ties that to the spare-capacity fact from the stimulus, and gives the total profit effect rather than stopping at the per-unit figure.
- CReject — the order does not cover its full share of fixed overheads, since £4.50 is well below the £8.00 needed to fund the business's normal running costs
This applies full-cost thinking to a spare-capacity decision the fixed costs are irrelevant to — they're already committed either way. This is the exact fallacy the mechanism above derives and warns against.
- DAccept — any price above £0 for otherwise-idle capacity is better than earning nothing at all, so Aldergate should accept regardless of the price offered
This ignores the variable-cost threshold entirely — a price BELOW £3.00 variable cost would actually reduce profit (negative contribution), even though it's still 'more than £0.' The correct test is whether contribution is positive, not merely whether the price is positive.
Traps tested: Compares to normal price not variable cost · Full cost fallacy on short run decision · Ignores variable cost threshold
Lush's bath-soap range sells at £5.50 per unit; variable cost is £1.00 per unit. On 3,300,000 units sold in a month, what is total contribution?
- £14,850,000
Correct. Contribution per unit = £5.50 − £1.00 = £4.50. Total contribution = £4.50 × 3,300,000 = £14,850,000, confirmed directly from a genuine mark-scheme exemplar (June 2023 ER, Q1b).
- B£21,450,000
This adds selling price and variable cost together (£5.50+£1.00=£6.50) instead of subtracting, then multiplies by units — contribution is the GAP between the two figures, not their sum.
- C£18,150,000
This uses the bare selling price (£5.50 × 3,300,000) without subtracting variable cost at all — it's total REVENUE, not total contribution.
- D£4.50
This is the correct contribution PER UNIT, but it stops there — the question asks for TOTAL contribution, which needs that figure multiplied by the 3,300,000 units actually sold.
Traps tested: Sign error added not subtracted · Forgot to subtract vc · Forgot to multiply by units
Practice this for real
This site teaches the mechanism; the exam is sat on Pearson's own real questions. Go find and attempt these yourself — nothing here substitutes for actually sitting a timed paper.
- Mark scheme
- Oct 2024 · Q2 — cited directly in this lesson
- Examiner report
- June 2022 · Q2 — cited directly in this lesson
- Examiner report
- June 2023 · Q1b — cited directly in this lesson
Select International Advanced Level → Business → any series, then look for WBS13.
Up next
Influences on Business Decisions
A firm's corporate culture isn't the values poster on the wall — it's whatever actually gets rewarded, which is why Handy's four culture types come from just two honest questions, not four labels to memorise. And the sharpest disagreement inside any boardroom often isn't about the facts at all — it's about which of two theories the firm even exists to serve: maximising its owners' return, or balancing everyone its decisions touch.
42 min