Strategic Cost Management · Relevant Cost Analysis

Limiting Factor and Product Mix Decisions Explained

Updated 11 October 2026 · Fact-checked

A limiting factor is the scarce resource that caps output, such as machine hours or material. When it binds, rank products by contribution per unit of that resource, not per unit of product. Allocate the resource to the highest-ranked product first, up to its demand limit, then move down. With two or more constraints, use a graphical or LP method.

Understand Limiting Factor and Product Mix Decisions

Every business has limits. Machine hours, skilled labour, a special material or cash can run short. The resource that stops you making and selling as much as you would like is the limiting factor (also called the key factor or scarce resource). In the short run, with fixed costs unchanged, the aim is to earn the highest total contribution from the limited resource.

The usual instinct is to push the product with the highest contribution per unit. That is wrong when products use the scarce resource in different amounts. A product that earns ₹80 but needs 4 hours earns less per hour than one that earns ₹60 and needs 2 hours. So the right yardstick is contribution per unit of limiting factor.

Fixed costs are ignored in the ranking because they do not change with the mix in the short run. Only variable (relevant) costs matter. Maximising total contribution then also maximises profit, as fixed costs stay the same.

With one limiting factor the method is a simple ranking. You fill the scarce resource with the best-ranked product up to its maximum demand, then the next, until the resource runs out. The last product made may be only partly supplied. With two or more constraints, ranking may not work, and you must use linear programming, usually the graphical method in exams.

The approach also gives an opportunity cost (shadow price) of the scarce resource. With one constraint, it is the contribution per unit of the resource from the best product you would have to give up for one more unit of resource. It helps you judge whether to buy extra capacity, subcontract or pay a premium.

Key rules to remember

Contribution per unit: Contribution per unit = Selling price per unit − Variable cost per unit; Use only variable costs. Ignore fixed costs, apportioned overheads and sunk costs.
Contribution per unit of limiting factor: Contribution per limiting factor unit = Contribution per unit ÷ Units of scarce resource used per unit of product; Rank products from highest to lowest on this figure. Use it only when one resource is the single binding constraint.
Resource requirement: Resource needed = Units produced × Resource per unit; Compare total need at full demand with availability to confirm that the constraint actually binds.
Total contribution and profit: Profit = Σ (Units × Contribution per unit) − Fixed costs; Fixed costs are deducted once, after choosing the mix.
Opportunity cost of the scarce resource (one constraint): Value of one extra unit of resource = Contribution per unit of resource of the marginal (last-ranked, partly produced) product; Valid for one constraint. Maximum price for extra resource = normal price per unit of resource + this opportunity value.
Two-constraint LP model: Maximise Z = c₁x₁ + c₂x₂ subject to a₁x₁ + a₂x₂ ≤ A, b₁x₁ + b₂x₂ ≤ B, x₁, x₂ ≥ 0; Check every corner point of the feasible region. The best one gives the optimal mix.

How to solve Limiting Factor and Product Mix Decisions questions

Use this sequence for any limiting factor or product mix question. It works for one constraint directly and leads into LP for two.

1Read the question and list the resources with their availability. Note maximum demand for each product and any minimum supply commitments.
2Compute contribution per unit for each product using variable costs only.
3Check whether the constraint binds: multiply maximum demand by resource per unit and compare the total with availability. If demand can be met in full, there is no limiting factor.
4For one binding constraint, compute contribution per unit of the scarce resource and rank the products.
5Allocate the resource in rank order, giving each product its maximum demand, until the resource is used up. Meet any compulsory minimum commitments first.
6Compute the total contribution, deduct fixed costs, and state the profit.
7For two or more constraints, write the LP: objective, constraints and non-negativity. Find the corner points, evaluate the objective at each, and select the highest.
8State a clear recommendation: the units of each product, the total contribution, and any comment on the opportunity cost of the scarce resource.

Quickest way: Rank, fill and verify in a four-column table

When to use it: Use when exactly one resource is scarce and the question gives per-unit data and demand limits.

Draw a table with columns: Product, Contribution per unit, Resource per unit, Contribution per resource unit.
Fill the last column and number the ranks.
Starting at rank 1, multiply demand by resource per unit, subtract from the remaining resource, and stop when it runs out. Compute the partial quantity for the last product as remaining resource ÷ resource per unit.
Multiply units by contribution per unit, add up, subtract fixed costs, and check that the resource used equals the total available.

Common mistakes in Limiting Factor and Product Mix Decisions

Ranking products by contribution per unit or by profit margin instead of contribution per scarce resource unit.
Contribution per unit feels like the natural measure of profitability, and it works when there is no constraint.
Fix: First identify the limiting factor. Then divide each product's contribution by its use of that factor and rank on that figure only.
Including fixed overheads or absorbed costs in the per-unit cost when computing contribution.
Questions often give full cost per unit, and students subtract the whole figure.
Fix: Use only variable costs. Treat fixed costs as irrelevant to the ranking and deduct them once at the end for profit.
Producing beyond the maximum demand for the top-ranked product.
Students pour all of the scarce resource into rank 1 and forget the demand cap.
Fix: Cap each product at its maximum sales. Move to the next rank once the cap is reached.
Ignoring minimum supply commitments or contractual orders.
The commitment is hidden in a note below the table.
Fix: Deduct the resource needed for committed units first, then rank and allocate what is left.
Using the ranking method when two or more constraints bind.
The one-constraint method is quick, so students apply it everywhere.
Fix: If two resources are both fully used or the ranking differs by resource, formulate an LP and test the corner points.
Not checking whether the constraint binds, or forgetting the opportunity cost of the scarce resource in a follow-up part.
Students start calculating without comparing total demand against availability, and skip the extra-resource sub-question.
Fix: Compute total resource needed at full demand first. For extra-resource parts, add the marginal product's contribution per resource unit to the normal price per unit.

Worked examples

Example 1

Meenakshi Components Ltd makes products A, B and C. Machine hours are limited to 3,800 per month. Fixed costs are ₹30,000 per month. Data per unit: A: selling price ₹200, variable cost ₹120, 4 machine hours, maximum demand 500 units. B: selling price ₹150, variable cost ₹90, 2 machine hours, maximum demand 600 units. C: selling price ₹135, variable cost ₹90, 3 machine hours, maximum demand 400 units. Find the optimal product mix, the monthly profit, and the opportunity cost of one machine hour.

Show the solution

Contribution per unit: A = 200 − 120 = ₹80; B = 150 − 90 = ₹60; C = 135 − 90 = ₹45.
Check the constraint: hours needed at full demand = A 500 × 4 = 2,000; B 600 × 2 = 1,200; C 400 × 3 = 1,200; total 4,400 hours. This is more than 3,800, so machine hours are the limiting factor.
Contribution per machine hour: A = 80 ÷ 4 = ₹20; B = 60 ÷ 2 = ₹30; C = 45 ÷ 3 = ₹15. Ranking: B first, A second, C third.
Allocate: B 600 units use 1,200 hours; remaining 2,600. A 500 units use 2,000 hours; remaining 600. C gets 600 hours, so 600 ÷ 3 = 200 units (demand 400, so partly met).
Contribution: B 600 × 60 = ₹36,000; A 500 × 80 = ₹40,000; C 200 × 45 = ₹9,000. Total = ₹85,000.
Profit = 85,000 − 30,000 = ₹55,000.
Opportunity cost of one machine hour = contribution per hour of the marginal product C = ₹15.

Answer: Make 600 units of B, 500 units of A and 200 units of C. Total contribution is ₹85,000 and profit is ₹55,000. One extra machine hour is worth ₹15 of contribution, so the firm should pay no more than its normal hourly variable cost plus ₹15 for additional hours.

Example 2

Kaveri Industries makes X and Y. Contribution is ₹30 per unit of X and ₹40 per unit of Y. Each unit of X needs 2 machine hours and 4 labour hours. Each unit of Y needs 3 machine hours and 2 labour hours. Available per period: 120 machine hours and 160 labour hours. Find the mix that maximises contribution.

Show the solution

Formulate: Maximise Z = 30X + 40Y subject to 2X + 3Y ≤ 120 (machine), 4X + 2Y ≤ 160 (labour), X, Y ≥ 0.
Axis intercepts: Machine line meets the X-axis at 60 and the Y-axis at 40. Labour line meets the X-axis at 40 and the Y-axis at 80.
Feasible corner points on the axes: (0, 0), (40, 0) since labour limits X to 40, and (0, 40) since machine limits Y to 40.
Intersection of both constraints: 2X + 3Y = 120 and 4X + 2Y = 160. Double the first: 4X + 6Y = 240. Subtract the second: 4Y = 80, so Y = 20. Then X = (120 − 60) ÷ 2 = 30. Check labour: 120 + 40 = 160. Check machine: 60 + 60 = 120.
Evaluate Z: (0, 0) = ₹0; (40, 0) = 30 × 40 = ₹1,200; (0, 40) = 40 × 40 = ₹1,600; (30, 20) = 900 + 800 = ₹1,700.
The highest value is at (30, 20). Both resources are fully used. Shadow prices from 2a + 4b = 30 and 3a + 2b = 40 give b = ₹1.25 per labour hour and a = ₹12.50 per machine hour. Check: 120 × 12.5 + 160 × 1.25 = 1,500 + 200 = ₹1,700.

Answer: Produce 30 units of X and 20 units of Y for a maximum contribution of ₹1,700. Machine hours are worth ₹12.50 each and labour hours ₹1.25 each at the margin.

Exam tips

Always test whether the constraint binds before ranking. Stating that demand needs 4,400 hours against 3,800 available earns method marks.
Show the ranking table clearly with the contribution per scarce unit column. Examiners follow it step by step.
Read notes for minimum supply commitments, outside purchase options and fixed costs. These change the allocation.
In two-constraint questions, list all corner points and show the objective value at each. Do not stop at the intersection point.
End with a one-line recommendation and, if asked, the opportunity cost or the maximum price for extra resource.

Practice questions from Relevant Cost Analysis

Limiting Factor and Product Mix Decisions 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 and Product Mix Decisions: frequently asked questions

What is the difference between limiting factor and key factor?

They mean the same thing: the resource whose scarcity limits output or sales. It can be machine hours, labour hours, material, or even sales demand. The decision rule is the same: maximise contribution per unit of that factor.

Why do we ignore fixed costs in limiting factor analysis?

In the short run fixed costs stay the same whatever mix you choose. So they cannot change which mix gives the best result. You deduct them once at the end only to state the profit.

When can I not use contribution per limiting factor ranking?

The ranking method is reliable only with one binding constraint. If two or more resources are scarce, the best product on one resource may be worst on the other. Use linear programming, usually the graphical method, in that case.

How do I find the opportunity cost of the scarce resource?

With one constraint, take the contribution per resource unit of the marginal product, the last one you are producing partly. That is the value of one more unit. With two constraints, the shadow prices come from the LP solution.