Limiting factors: choosing the best product mix

The method

1. Check that the resource really is limiting: total needed to meet all demand > amount available.

2. Calculate contribution per unit for each product.

3. Divide by the amount of the limiting factor each unit uses: contribution per unit of limiting factor (per kg, per labour hour, per machine hour).

4. Rank products from highest to lowest on this measure (not on contribution per unit).

5. Allocate the scarce resource in rank order, meeting full demand for each product until the resource runs out.

6. Calculate total contribution, then deduct fixed costs for profit.

If a minimum quantity of a product must be made (a contract), allocate resource to that first.

Worked example

Material is limited to 5,000 kg.

Points to watch

Product Y has the highest contribution per unit (£30) but the lowest per kg, so it is made last. Total kg needed to meet all demand = 2,000 + 2,000 + 1,800 = 5,800 kg, more than the 5,000 available, so material is limiting.

Other factors: customers may want a full range (dropping Y could lose customers for X and Z); the limit may be temporary (find another supplier, overtime); quality and marketing considerations.

Worked example

Explain the production plan in the table.

1. Rank by contribution per kg: X (£5.00), Z (£4.00), Y (£3.00)
2. Make all 500 of X using 2,000 kg, then all 300 of Z using 1,800 kg
3. Remaining 1,200 kg makes 120 units of Y

Answer: Total contribution £20,800

Check yourself

1. A product sells for £45 with variable costs of £27. It needs 3 machine hours per unit. Calculate the contribution per machine hour.
   Show answer

   £6.00. Contribution £18 / 3 hours = £6 per hour.

2. After making the top-ranked product, 1,350 labour hours remain. The next product needs 4.5 hours per unit and has demand of 400 units. How many units can be made?
   Show answer

   300 units. 1,350 / 4.5 = 300 units (below demand of 400).

3. Products P and Q each use 2 kg of material. P has contribution £10 per unit, demand 600; Q has contribution £7 per unit, demand 800. Only 2,000 kg is available. Calculate the maximum total contribution.
   Show answer

   £8800. P first: 600 units use 1,200 kg (£6,000); 800 kg left makes 400 Q (£2,800); total £8,800.

4. Products need 3 hours (demand 1,000), 2 hours (demand 1,500) and 5 hours (demand 400) per unit. How many labour hours are needed to meet all demand?
   Show answer

   8000 hours. 3,000 + 3,000 + 2,000 = 8,000 hours.

5. Product A has contribution £40 per unit using 8 kg; product B has £25 per unit using 4 kg. Material is the limiting factor. Which should be made first?
   • B, because it earns £6.25 per kg against A's £5.00
   • A, because its contribution per unit is higher
   • The same number of units of each product
   • Neither, until more material is found
   Show answer

   B, because it earns £6.25 per kg against A's £5.00. Rank on contribution per kg when kg are scarce.

6. A contract requires 200 units of the lowest-ranked product. How should this be handled?
   • Ignore the contract
   • Make only that product
   • Allocate resource to the 200 contracted units first, then rank the rest
   • Make it last as usual
   Show answer

   Allocate resource to the 200 contracted units first, then rank the rest. Contractual commitments must be met before optimising the rest.

7. Which is a reason not to drop the lowest-ranked product completely?
   • Customers may want the full range and stop buying the other products
   • It has the lowest contribution per kg
   • It uses the most material
   • Fixed costs would rise
   Show answer

   Customers may want the full range and stop buying the other products. Products are often bought together.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting specification (XAC11/YAC11), Issue 2

Last updated 8 November 2026. Spotted a mistake? Tell us.