Special orders and limiting factors
Short-term decisions use contribution: fixed costs arise anyway and do not change the decision.
Formulas
- Minimum price with spare capacity = variable cost per unit
- Accept a special order if its contribution is positive
- With a limiting factor, rank by contribution per unit of that factor
Your turn
Three problems on this topic. Amounts with or without thousands separators, a point for pence.
Task
A firm has spare capacity. Normal price £46.50, variable cost £24.00 per unit, fixed costs £39,000.00 at 4,000 units (full cost £33.75 per unit). A customer offers £30.00 each for an extra order of 600 units; capacity is enough and normal sales stay the same.
Short-term minimum price per unit in £
Contribution of the extra order in £ (negative with a minus)
Decision
Amounts like 12,500 or 12500.50; percentages as a number (12.5). Round to the penny or 2 decimal places.
Worked example
A firm has spare capacity. Normal price £73.00, variable cost £41.00 per unit, fixed costs £25,000.00 at 3,400 units (full cost £48.35 per unit). A customer offers £46.00 each for an extra order of 1,000 units; capacity is enough and normal sales stay the same.
Worked solution
- 1.With spare capacity the fixed costs arise anyway; only variable costs matter.
- 2.Minimum price = variable cost = £41.00
- 3.Contribution = (£46.00 − £41.00) × 1,000 = £5,000.00 → accept
Typical mistake: Deciding on full cost per unit and rejecting an order with a positive contribution.
The bottleneck machine has 7,100 minutes available. Plan the product mix with the highest contribution (whole units only).
| Product | Price | Variable cost | Min/unit | Max sales |
|---|---|---|---|---|
| A | £31.50 | £24.50 | 12 | 300 |
| B | £94.00 | £68.00 | 11 | 2,000 |
| C | £48.50 | £33.50 | 2 | 1,900 |
Worked solution
- 1.Contribution per minute: A £7.00 / 12 = £0.58; B £26.00 / 11 = £2.36; C £15.00 / 2 = £7.50
- 2.Ranking by contribution per minute: C → B → A
- 3.C: 1,900 units × 2 min = 3,800 min; remaining 3,300 min for B: 300 units; A is dropped
- 4.Contribution = 1,900 × £15.00 + 300 × £26.00 = £36,300.00
Typical mistake: Ranking by contribution per unit instead of contribution per bottleneck minute.
Frequently asked questions
Why ignore fixed costs for a special order?
They arise with or without the order; every pound above variable cost improves the result.