Performance Management · Make-or-buy and other short-term decisions

Limiting Factor Analysis for ACCA PM

Updated 11 October 2026 · Fact-checked

Limiting factor analysis finds the production plan that earns the most contribution when one resource is short. Calculate contribution per unit of the scarce resource for each product, rank them, then make products in rank order up to maximum demand until the resource runs out.

Understand Limiting Factor Analysis

A limiting factor (or key factor) is a resource that stops you from making or selling as much as you would like. It can be machine hours, labour hours, materials, or even sales demand. In the exam it is usually a production resource.

If there is no limit, you simply make everything you can sell, and contribution per unit of product is a fair guide. When a resource is short, that guide fails. A product with a high contribution per unit may use up a lot of the scarce resource and crowd out other products.

The right question is: how much contribution do I earn from each unit of the scarce resource? A product earning $12 per machine hour beats one earning $10 per hour, even if its contribution per unit is lower. Each hour is worth more in the first product.

So you rank products by contribution per unit of limiting factor. You then fill the available resource in that order, never going beyond the maximum demand for each product. The last product may be made only in part, because the resource runs out.

The method assumes fixed costs are the same whatever the plan, so you maximise total contribution, not profit per unit. It also assumes only one resource is short. With two or more constraints you need linear programming.

Key rules to remember

Contribution per unit: Contribution per unit = selling price per unit − variable cost per unit; Use only variable costs. Exclude fixed overheads and absorbed fixed costs.
Contribution per unit of limiting factor: Contribution per limiting factor unit = contribution per unit ÷ units of scarce resource used per unit of product; This is the ranking measure. Higher is better.
Resource needed for a product: Resource used = units produced × resource per unit; Use maximum demand for units when you allocate the resource in rank order.
Total contribution of the plan: Total contribution = Σ (units made × contribution per unit); Subtract fixed costs only if the question asks for profit.
Value of extra scarce resource: Maximum price worth paying per extra unit = normal price + contribution per unit of resource earned by the marginal product; The marginal product is the one that is only partly made. This links to shadow prices.

How to solve Limiting Factor Analysis questions

Use this method for any single limiting factor question, including those with maximum demand.

1Identify the limiting factor. Compare the resource needed to meet maximum demand with the resource available. If need exceeds supply, that resource is limiting.
2Calculate the contribution per unit for each product: selling price less variable costs only.
3Divide each contribution by the units of scarce resource used per unit. This gives contribution per limiting factor unit.
4Rank the products from highest to lowest contribution per limiting factor unit.
5Allocate the resource in rank order. Make each product up to its maximum demand, using units × resource per unit, until the resource is used up.
6For the last product, divide the remaining resource by its usage per unit. This gives the units you can make. Use whole units only if the question says so.
7Calculate total contribution from the plan. Deduct fixed costs if the question asks for profit.
8Answer the question asked. Add a brief comment on non-financial factors, such as customers lost or whether a product is a loss leader, if the requirement asks for it.

Quickest way: Rank, fill, check

When to use it: Use in Section B or C questions with three or four products, one scarce resource and given maximum demands.

Write a small table with one column per product. Rows: contribution per unit, resource per unit, contribution per resource unit, rank.
Check the resource total needed at maximum demand against the amount available. If it fits, there is no limiting factor.
Work down the ranking. Write the resource used and the resource left after each product. The remaining amount tells you immediately when to stop.
Check your answer: resource used must equal resource available, and no product may exceed its maximum demand.
Total contribution can also be checked using the last product: remaining resource × its contribution per resource unit.

Common mistakes in Limiting Factor Analysis

Ranking by contribution per unit of product instead of per unit of scarce resource.
Contribution per unit is the number students calculate first, and it looks like the answer.
Fix: Always divide by the resource used per unit before ranking. Write the ranking line in your table so you cannot skip it.
Ignoring maximum demand and making the top-ranked product until the resource runs out.
Students read the ranking as 'make as much of the best product as possible'.
Fix: Cap each product at maximum demand. Only the lowest-ranked product made should be limited by the resource rather than by demand.
Including fixed costs or absorbed overheads in the contribution per unit.
Standard cost cards show a full absorption cost, and students use the total cost figure.
Fix: Use only variable costs: direct materials, direct labour if variable, and variable overheads. Fixed overheads are not relevant to the ranking.
Ranking by the number of units of the scarce resource per unit, or by ratio inverted (resource per $ of contribution).
Students divide the wrong way round.
Fix: Contribution is always the numerator. A higher result means a better use of the resource.
Making a part-unit when the question requires whole units, or leaving spare resource without explanation.
Rushing the last step.
Fix: Re-read the question for 'whole units' and 'batch sizes'. Check that resource used equals resource available.
Applying the single limiting factor method when two resources are scarce.
Students stop after finding one constraint.
Fix: Test every resource against maximum demand first. If more than one is short, state that linear programming is needed and use a graph or simultaneous equations.

Worked examples

Example 1

A company makes three products using machine hours, which are limited to 1,800 hours a month. Product A: selling price $50, variable cost $30, 2 machine hours per unit, maximum demand 400 units. Product B: selling price $40, variable cost $28, 1 machine hour per unit, maximum demand 500 units. Product C: selling price $60, variable cost $36, 3 machine hours per unit, maximum demand 300 units. Find the production plan that maximises contribution, and the total contribution.

Show the solution

Check the constraint. Hours needed at maximum demand: A 400 × 2 = 800; B 500 × 1 = 500; C 300 × 3 = 900. Total = 2,200 hours, which exceeds 1,800. Machine hours are limiting.
Contribution per unit: A = 50 − 30 = $20; B = 40 − 28 = $12; C = 60 − 36 = $24.
Contribution per machine hour: A = 20 ÷ 2 = $10; B = 12 ÷ 1 = $12; C = 24 ÷ 3 = $8.
Ranking: B first ($12), A second ($10), C third ($8).
Allocate hours. B: 500 units use 500 hours; 1,300 hours left. A: 400 units use 800 hours; 500 hours left. C: 500 ÷ 3 = 166.67 units use the remaining 500 hours.
Contribution: B 500 × 12 = $6,000; A 400 × 20 = $8,000; C 500 hours × $8 = $4,000 (166.67 × 24).
Total = 6,000 + 8,000 + 4,000 = $18,000.

Answer: Make 500 units of B, 400 units of A and 166.67 units of C (about 167 if only whole units are allowed). Total contribution is $18,000.

Example 2

A company has 8,000 kg of material available. Material costs $10 per kg. Product P: selling price $90, variable cost $60 (includes 3 kg of material), maximum demand 1,000 units. Product Q: selling price $70, variable cost $45 (includes 2 kg), maximum demand 1,500 units. Product R: selling price $110, variable cost $80 (includes 4 kg), maximum demand 800 units. Fixed costs are $40,000. Find the optimal plan, the profit, and the most the company should pay per kg for extra material.

Show the solution

Check the constraint. Material at maximum demand: P 1,000 × 3 = 3,000 kg; Q 1,500 × 2 = 3,000 kg; R 800 × 4 = 3,200 kg. Total = 9,200 kg, above 8,000 kg. Material is limiting.
Contribution per unit: P = 90 − 60 = $30; Q = 70 − 45 = $25; R = 110 − 80 = $30.
Contribution per kg: P = 30 ÷ 3 = $10; Q = 25 ÷ 2 = $12.50; R = 30 ÷ 4 = $7.50.
Ranking: Q first, P second, R third.
Allocate material. Q: 1,500 units use 3,000 kg; 5,000 kg left. P: 1,000 units use 3,000 kg; 2,000 kg left. R: 2,000 ÷ 4 = 500 units.
Contribution: Q 1,500 × 25 = $37,500; P 1,000 × 30 = $30,000; R 500 × 30 = $15,000. Total = $82,500.
Profit = 82,500 − 40,000 = $42,500.
Extra material would be used to make more R, which earns $7.50 per kg after paying the normal $10. So the company could pay up to 10 + 7.50 = $17.50 per kg, as long as R stays below its maximum demand of 800 units (300 more units, so up to 1,200 extra kg).

Answer: Make 1,500 Q, 1,000 P and 500 R. Contribution is $82,500 and profit is $42,500. The company should pay up to $17.50 per kg for extra material, for up to 1,200 extra kg.

Exam tips

In Section B objective test cases, the question often asks for only one number, such as the rank of a product or the units of the last product. Do the whole table anyway. It is quick and avoids errors.
Read the data carefully for fixed costs and absorbed overheads. They are distractors in ranking questions.
In Section C, set out the table clearly: contribution per unit, resource per unit, contribution per resource unit, rank. Markers award marks for each step even if one figure is wrong.
If the question asks for comment, mention that the plan may drop products that customers want, and that the analysis is for the short term with one constraint only.
Always check that your plan uses exactly the resource available and respects every maximum demand.

Practice questions from Make-or-buy and other short-term decisions

Limiting Factor Analysis in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Limiting Factor Analysis: frequently asked questions

What is a limiting factor in ACCA PM?

It is a resource, such as machine hours, labour or materials, that restricts output below what demand would allow. Only one limiting factor can be handled with the ranking method. With more than one, you need linear programming.

How do I rank products by contribution per limiting factor?

Divide each product's contribution per unit by the units of scarce resource it uses. Rank from highest to lowest. Then make products in that order, up to their maximum demand, until the resource runs out.

What if maximum demand is given in the question?

Cap each product at its maximum demand when allocating the resource. Move to the next ranked product once demand is met. The last product may be made in part, using the remaining resource.

Do fixed costs affect limiting factor analysis?

No, not for the ranking. Fixed costs are assumed to be the same whatever the plan. Deduct them from total contribution only if you are asked for profit.