Best product mix with a limiting factor
With a limiting factor, rank by contribution per unit of that factor, not by unit contribution.
Worked example
The bottleneck machine has 16,800 minutes available. Plan the product mix with the highest contribution (whole units only).
| Product | Price | Variable cost | Min/unit | Max sales |
|---|---|---|---|---|
| A | £53.50 | £32.00 | 13 | 1,900 |
| B | £60.50 | £27.00 | 11 | 800 |
| C | £58.00 | £21.50 | 20 | 700 |
Worked solution
- 1.Contribution per minute: A £21.50 / 13 = £1.65; B £33.50 / 11 = £3.05; C £36.50 / 20 = £1.83
- 2.Ranking by contribution per minute: B → C → A
- 3.B: 800 units × 11 min = 8,800 min; remaining 8,000 min for C: 400 units; A is dropped
- 4.Contribution = 800 × £33.50 + 400 × £36.50 = £41,400.00
Typical mistake: Ranking by contribution per unit instead of contribution per bottleneck minute.
Your turn
Three problems of exactly this type, each time with new numbers. Amounts with or without thousands separators.
Task
The bottleneck machine has 23,600 minutes available. Plan the product mix with the highest contribution (whole units only).
| Product | Price | Variable cost | Min/unit | Max sales |
|---|---|---|---|---|
| A | £45.50 | £36.00 | 16 | 1,300 |
| B | £81.50 | £58.00 | 5 | 1,600 |
| C | £93.00 | £40.00 | 13 | 1,400 |
Which product is scheduled first?
Quantity of C in the best mix
Total contribution in £
Amounts like 12,500 or 12500.50; percentages as a number (12.5). Round to the penny or 2 decimal places.
Formulas for this topic
- 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
Typical mistake: Ranking by contribution per unit instead of contribution per bottleneck minute.
Frequently asked questions
What is the typical mistake in "Best product mix with a limiting factor"?
Ranking by contribution per unit instead of contribution per bottleneck minute.
Why ignore fixed costs for a special order?
They arise with or without the order; every pound above variable cost improves the result.