Performance Management · Limiting factors

Single Limiting Factor: Contribution per Unit of Scarce Resource

Updated 11 October 2026 · Fact-checked

With one scarce resource, calculate each product's contribution per unit of that resource, rank the products from highest to lowest, and make them in that order until the resource runs out. Respect any demand limits. This plan gives the highest total contribution.

Understand Single Limiting Factor: Contribution per Unit of Scarce Resource

A limiting factor (or key factor) is a resource that is in short supply and stops you making or selling as much as you want. It could be labour hours, machine hours, material or even sales demand. If you could make unlimited units of every product, you would simply make as many as the market takes. A shortage forces a choice.

The usual ranking by contribution per unit of product can mislead you. A product with a high contribution per unit may use a lot of the scarce resource. Another product may earn less per unit but use very little of it. Because the resource is the thing that runs out, you want the most contribution from each unit of it.

That is why you calculate contribution per unit of limiting factor. Rank products on this figure. Give the scarce resource to the top-ranked product first, up to its maximum demand. Then move to the next, and so on, until the resource is used up. The last product may be made only in part.

This method works because fixed costs are the same whatever you produce, so maximising total contribution also maximises profit. It is a short-term decision tool. It assumes only one resource is scarce, that variable cost per unit is constant, and that you can make products in any quantity within demand limits.

Key rules to remember

Contribution per unit: Contribution per unit = Selling price per unit − Variable cost per unit; Use variable costs only. Ignore fixed overheads and absorbed overheads.
Contribution per unit of limiting factor: Contribution per unit of limiting factor = Contribution per unit ÷ Units of scarce resource used per unit; This is the ranking measure. Higher is better.
Resource needed for a product: Resource required = Units to make × Resource per unit; Compare with the resource still available before allocating.
Total contribution of the plan: Total contribution = Σ (units made × contribution per unit); Deduct fixed costs only if the question asks for profit.

How to solve Single Limiting Factor: Contribution per Unit of Scarce Resource questions

Use this method for any single limiting factor question. Keep the working in a small table so you can check it quickly.

1Check that only one resource is scarce. Compare the resource needed for maximum demand with the amount available.
2Calculate contribution per unit for each product: selling price less variable costs.
3Divide each contribution by the units of scarce resource used per unit.
4Rank the products from highest to lowest contribution per unit of scarce resource.
5Allocate the resource in rank order. Make each product up to its maximum demand until the resource runs out.
6Work out the units of the last product from the remaining resource. This may be a part-production.
7Calculate total contribution from the plan. Deduct fixed costs if the question asks for profit.
8Note any assumptions or limits, such as the plan being short-term or demand being uncertain.

Quickest way: Rank, fill, stop

When to use it: Use it for any objective test or short written question with one scarce resource and several products.

Write contribution per unit and resource per unit for each product in one line.
Divide to get contribution per unit of resource. Circle the ranking.
Subtract resource used by each product in turn from the total available.
Stop when the balance is too small for full demand. Divide the balance by resource per unit.
Multiply units by contribution per unit and add up. Do not forget fixed costs if profit is asked.

Common mistakes in Single Limiting Factor: Contribution per Unit of Scarce Resource

Ranking products by contribution per unit instead of per unit of scarce resource.
Contribution per unit is the first figure you calculate, so it feels like the answer.
Fix: Always divide by the scarce resource used per unit before you rank.
Using profit per unit or including absorbed fixed overheads in the calculation.
The question gives a full cost per unit, and students use it without checking.
Fix: Strip the cost back to variable costs only. Fixed costs do not change with the decision.
Ignoring the maximum demand for the top-ranked product.
Students want to use all the resource on the best product.
Fix: Cap each product at its demand limit, then pass the remaining resource down the ranking.
Not checking whether the resource is actually limiting.
Students assume a shortage exists because the question is in this chapter.
Fix: Calculate the resource needed for full demand. If it is within the available amount, there is no limiting factor.
Making whole units only when the question allows part-production, or the reverse.
Students round without reading the wording.
Fix: Read whether units are divisible. Show the exact figure and state any rounding you apply.
Treating labour as a variable cost when it is fixed, or the reverse, in the contribution calculation.
Students do not read the cost behaviour given in the scenario.
Fix: Check how each cost behaves. If labour is paid regardless of output, leave it out of contribution and note the point.

Worked examples

Example 1

A company makes three products using one scarce material, of which 2,600 kg are available. Data per unit: Product A: selling price ₹90, variable cost ₹50, material 4 kg. Product B: selling price ₹70, variable cost ₹40, material 2 kg. Product C: selling price ₹120, variable cost ₹72, material 6 kg. Maximum demand: A 300 units, B 400 units, C 200 units. Find the production plan that maximises contribution and the total contribution.

Show the solution

Check the resource needed for full demand: A 300 × 4 = 1,200 kg; B 400 × 2 = 800 kg; C 200 × 6 = 1,200 kg. Total 3,200 kg, which is more than 2,600 kg. Material is limiting.
Contribution per unit: A = 90 − 50 = ₹40; B = 70 − 40 = ₹30; C = 120 − 72 = ₹48.
Contribution per kg: A = 40 ÷ 4 = ₹10; B = 30 ÷ 2 = ₹15; C = 48 ÷ 6 = ₹8.
Ranking: B first (₹15), A second (₹10), C third (₹8).
Allocate: B 400 units uses 800 kg, leaving 1,800 kg. A 300 units uses 1,200 kg, leaving 600 kg. C gets 600 kg, so 600 ÷ 6 = 100 units.
Total contribution: B 400 × 30 = ₹12,000; A 300 × 40 = ₹12,000; C 100 × 48 = ₹4,800. Total = ₹28,800.

Answer: Make 400 units of B, 300 units of A and 100 units of C. Total contribution is ₹28,800.

Example 2

A firm makes two products, X and Y, using skilled labour hours, of which 1,000 are available. Data per unit: X: selling price ₹200, materials ₹60, variable labour and overhead ₹40, 2 hours. Y: selling price ₹150, materials ₹50, variable labour and overhead ₹20, 1 hour. Maximum demand: X 300 units, Y 600 units. Fixed costs are ₹30,000. Calculate the maximum profit.

Show the solution

Contribution per unit: X = 200 − 60 − 40 = ₹100; Y = 150 − 50 − 20 = ₹80.
Check the resource: X 300 × 2 = 600 hours; Y 600 × 1 = 600 hours. Total 1,200 hours, more than 1,000. Labour hours are limiting.
Contribution per hour: X = 100 ÷ 2 = ₹50; Y = 80 ÷ 1 = ₹80.
Ranking: Y first (₹80), X second (₹50).
Allocate: Y 600 units uses 600 hours, leaving 400 hours. X gets 400 hours, so 400 ÷ 2 = 200 units.
Total contribution: Y 600 × 80 = ₹48,000; X 200 × 100 = ₹20,000. Total = ₹68,000.
Profit = 68,000 − 30,000 = ₹38,000.

Answer: Make 600 units of Y and 200 units of X. Maximum profit is ₹38,000.

Exam tips

In objective test questions, the ranking is often the only thing tested. Calculate contribution per unit of scarce resource first and check the option wording against it.
Always test whether the resource is really limiting by comparing the requirement at full demand with availability. A quick check can save a lot of work.
In a constructed-response question, show a neat table of contribution, resource use, per-unit-of-resource figures and ranking. Marks are given for method even if one figure is wrong.
Read the question for demand limits, part-units and whether profit or contribution is required. Those details change the final answer.
If asked for comments, mention that the plan is short-term, relies on stable costs and demand, and that other options such as buying in or getting more resource may be worth considering.

Practice questions from Limiting factors

Single Limiting Factor: Contribution per Unit of Scarce Resource: frequently asked questions

How do you calculate contribution per limiting factor?

Find contribution per unit by deducting variable costs from selling price. Then divide by the units of scarce resource used by one unit of product. The result is contribution per unit of limiting factor, such as per machine hour.

Why not rank products by contribution per unit?

Because the scarce resource is what stops you producing more. A product with a high contribution per unit may use a lot of that resource and so earn less per hour or kg than a rival product. Ranking per unit of resource gives the highest total contribution.

What if the last product cannot be made in full?

Use the remaining resource to make as many units as it allows. Divide the balance by resource per unit. If part-units are not allowed, round down and state this.

Do fixed costs affect the production plan?

No. Fixed costs stay the same whichever plan you choose, so they do not affect the ranking. Deduct them only at the end if you need to find profit.