Performance Management · Limiting factors

Limiting Factors and Key Factor Analysis Explained

Updated 11 October 2026 · Fact-checked

A limiting factor is any scarce resource that stops a business making or selling as much as it wants. Key factor analysis finds the plan that earns the most profit despite the shortage. With one limiting factor, rank products by contribution per unit of the scarce resource and produce in that order.

Understand Limiting Factors and Key Factor Analysis

Every business wants to make and sell as much as it can. In practice something usually stops it. That something is a limiting factor, also called a key factor or scarce resource. It is the resource that runs out first and caps activity.

Common limiting factors are:
- Materials: a supplier can only deliver a fixed quantity.
- Labour: not enough skilled hours are available.
- Machine hours: capacity is fixed in the short term.
- Cash: not enough money to fund production or stock.
- Sales demand: the market will only buy so many units.

Why does it matter? Normally you judge products by contribution per unit. A product with a high contribution per unit looks best. But if resources are short, each unit of the scarce resource should earn as much contribution as possible. A product may earn a high contribution per unit yet use up a lot of the scarce resource. Another product may earn less per unit but use very little of the resource, so it gives more total contribution.

The rule is simple. Find the limiting factor. Calculate contribution per unit of that factor for each product. Rank the products. Make the highest-ranked product first, up to its maximum demand, then the next, until the resource runs out. This gives the maximum total contribution, and so maximum profit when fixed costs are unchanged.

This method works when there is one limiting factor and the products can be made in part-quantities as a plan. If there are two or more scarce resources, you need linear programming instead. Limits also change over time. Shortages are short-term problems. In the long term management can remove them by buying more machines, hiring staff or finding new suppliers.

Key rules to remember

Contribution per unit: Contribution per unit = Selling price per unit − Variable cost per unit; Use variable costs only. Fixed costs are ignored because they do not change with the production choice.
Contribution per unit of limiting factor: Contribution per limiting factor unit = Contribution per unit ÷ Units of scarce resource used per unit; For example contribution per machine hour or per kg of material. This is the ranking measure.
Resource needed for demand: Resource required = Maximum demand (units) × Resource per unit; Compare with the resource available to see whether it is truly limiting.
Limiting factor test: Resource is limiting if total required for maximum demand > resource available; Check this before ranking. If nothing is short, make everything demanded.
Ranking rule: Allocate resource in order of highest contribution per unit of scarce resource, up to maximum demand; Valid for a single limiting factor.

How to solve Limiting Factors and Key Factor Analysis questions

Use this method for any single limiting factor question. Keep the working in a small table.

1Calculate the contribution per unit for each product (selling price less variable costs).
2Work out the total resource needed to meet maximum demand for all products. Compare with the amount available to confirm there is a shortage.
3Calculate the resource used per unit of each product and then the contribution per unit of scarce resource.
4Rank the products. The highest contribution per unit of resource is rank 1.
5Allocate the resource to rank 1 up to its maximum demand, then rank 2, and so on until the resource is used up. The last product may be only partly made.
6Calculate the production plan in units and the total contribution.
7Deduct fixed costs if the question asks for profit.
8Comment on the result if asked, for example on other factors such as customer loyalty, or whether the shortage can be relieved.

Quickest way: Rank by contribution per scarce unit

When to use it: Use it when only one resource is short and the question gives the contribution and resource use for each product.

Write contribution per unit and resource per unit side by side for each product.
Divide to get contribution per scarce unit and rank straight away.
Fill demand in rank order, using a running total of the resource left.
Multiply units made by contribution per unit and add up. Stop when the resource is gone.

Common mistakes in Limiting Factors and Key Factor Analysis

Ranking products by contribution per unit instead of per unit of scarce resource.
Contribution per unit is the usual measure, so students use it out of habit.
Fix: Always ask what is scarce first, then divide contribution by the amount of that resource each unit uses.
Including fixed costs in the contribution calculation or ranking.
Students confuse contribution with profit per unit.
Fix: Use selling price less variable costs only. Subtract fixed costs once, at the end, if profit is asked for.
Not checking whether the resource is actually limiting.
Students assume the question must be a ranking one.
Fix: Compare total need at maximum demand with availability. If supply is enough, make everything demanded.
Exceeding maximum demand for the top-ranked product.
Students spend all of the resource on rank 1 because it is the best.
Fix: Cap each product at its demand limit, then move to the next ranking with the resource left.
Using the single-factor ranking when there are two or more scarce resources.
The method is learned first and applied automatically.
Fix: Count the constraints. If two or more bind, use linear programming and graph or simultaneous equations.
Treating an outsourced or bought-in product as having no scarce resource use, then forgetting extra cost when comparing.
Make-or-buy and limiting factors are mixed in one question.
Fix: Rank by the saving per unit of scarce resource: (buy-in price − variable cost of making) ÷ scarce resource per unit made.

Worked examples

Example 1

A company makes products X and Y. Selling price per unit: X ₹100, Y ₹140. Variable cost per unit: X ₹60, Y ₹80. Machine hours per unit: X 2, Y 4. Maximum demand: X 500 units, Y 300 units. Only 1,600 machine hours are available. Fixed costs are ₹20,000. Find the plan that maximises profit and the profit.

Show the solution

Contribution per unit: X = 100 − 60 = ₹40. Y = 140 − 80 = ₹60.
Hours needed for full demand: X 500 × 2 = 1,000. Y 300 × 4 = 1,200. Total 2,200 hours, more than 1,600 available, so machine hours are limiting.
Contribution per machine hour: X = 40 ÷ 2 = ₹20. Y = 60 ÷ 4 = ₹15.
Ranking: X first, Y second.
Make X up to demand: 500 units uses 1,000 hours. Hours left = 1,600 − 1,000 = 600.
Make Y with the 600 hours: 600 ÷ 4 = 150 units (below demand of 300).
Total contribution: X 500 × 40 = ₹20,000. Y 150 × 60 = ₹9,000. Total = ₹29,000.
Profit = 29,000 − 20,000 = ₹9,000.

Answer: Make 500 units of X and 150 units of Y. Total contribution is ₹29,000 and profit is ₹9,000.

Example 2

A firm makes three products A, B and C from one scarce material, of which 2,400 kg are available. Per unit: A sells for ₹90, variable cost ₹50, uses 4 kg. B sells for ₹120, variable cost ₹70, uses 5 kg. C sells for ₹75, variable cost ₹45, uses 2 kg. Maximum demand is 300 units of each product. Find the contribution-maximising production plan and total contribution.

Show the solution

Contribution per unit: A = 90 − 50 = ₹40. B = 120 − 70 = ₹50. C = 75 − 45 = ₹30.
Material for full demand: A 300 × 4 = 1,200. B 300 × 5 = 1,500. C 300 × 2 = 600. Total 3,300 kg, more than 2,400 kg, so material is limiting.
Contribution per kg: A = 40 ÷ 4 = ₹10. B = 50 ÷ 5 = ₹10. C = 30 ÷ 2 = ₹15.
Ranking: C first at ₹15 per kg. A and B tie at ₹10 per kg.
Make C: 300 units uses 600 kg. Left = 2,400 − 600 = 1,800 kg.
A and B tie, so the total contribution is the same whichever is made first. Make A: 300 units uses 1,200 kg. Left = 600 kg.
Make B with 600 kg: 600 ÷ 5 = 120 units.
Total contribution: C 300 × 30 = ₹9,000. A 300 × 40 = ₹12,000. B 120 × 50 = ₹6,000. Total = ₹27,000.
Check with the tie: 1,800 kg at ₹10 per kg = ₹18,000, plus C ₹9,000 = ₹27,000. This agrees.

Answer: Make 300 units of C, 300 units of A and 120 units of B (or any A/B split using 1,800 kg). Total contribution is ₹27,000.

Exam tips

In objective test questions, the first line of working should be contribution per unit of the scarce resource. Wrong ranking loses all the marks because there is no partial credit.
Read carefully for more than one constraint. Demand limits are not scarce resources for ranking, but they cap how much of each product you make.
Check the resource-needed-versus-available figure early. It confirms the resource is limiting and catches arithmetic errors.
In constructed response questions, show a clear table with contribution, resource use, contribution per unit of resource and rank. Then state the plan and the total contribution.
If asked to comment, mention non-financial points: dropping a product may upset customers, shortages may be temporary, and extra resource could be bought at a premium if the extra contribution per unit exceeds the premium.

Practice questions from Limiting factors

Limiting Factors and Key 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 Factors and Key Factor Analysis: frequently asked questions

What is a limiting factor in management accounting?

It is a scarce resource that limits the activity of a business, such as materials, labour hours, machine hours, cash or sales demand. It stops the firm from doing all it would like. Plans must be built around it.

Why do we rank by contribution per unit of the scarce resource?

Because the aim is to earn the most total contribution from a fixed amount of the resource. A product that earns the most per unit of that resource gives the best return for each unit used. Contribution per product unit hides how much of the resource is consumed.

What if there are two limiting factors?

The simple ranking method no longer works reliably. You use linear programming, which finds the best combination of products within all the constraints. ACCA PM covers this with graphs and shadow prices.

Are fixed costs relevant to limiting factor decisions?

No, not to the ranking, because fixed costs do not change with the production mix in the short term. You deduct them only at the end if you need to report profit.