Fenwick Engineering: ranking under a machine-hour constraint
Fenwick Engineering has 16,000 machine hours a year and makes three products on the same machines. P sells for £60, has variable cost £36 and uses 3 machine hours; maximum demand is 3,000 units, but a contract obliges Fenwick to supply at least 2,000 units. Q sells for £45, has variable cost £24 and uses 2 machine hours; maximum demand is 4,500 units. R sells for £38, has variable cost £26 and uses 1 machine hour; maximum demand is 3,000 units. Annual fixed costs are £120,000 and do not change with the product mix. An external supplier has offered to supply Fenwick with up to 900 units of Q at £38 each; Fenwick would sell them under its own brand, and the freed machine hours would be used to make more P.
1. Determine the optimal production plan and the resulting annual profit.
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Contribution per unit and per machine hour
| P | Q | R | |
|---|---|---|---|
| Price | 60 | 45 | 38 |
| Variable cost | (36) | (24) | (26) |
| Contribution per unit | 24 | 21 | 12 |
| Machine hours | 3 | 2 | 1 |
| Contribution per hour | 8.00 | 10.50 | 12.00 |
Ranking: R, then Q, then P - but the 2,000-unit P contract must be met first.
Plan
- Contract P: 2,000 units × 3 hrs = 6,000 hrs → contribution 2,000 × £24 = £48,000
- Remaining 10,000 hrs: R first - 3,000 units × 1 hr = 3,000 hrs → contribution £36,000
- Remaining 7,000 hrs: Q - 7,000 ÷ 2 = 3,500 units (within 4,500 demand) → contribution £73,500
Total contribution = 48,000 + 36,000 + 73,500 = £157,500 Less fixed costs £120,000 → profit £37,500
Unsatisfied demand: 1,000 units of P and 1,000 units of Q.
2. Evaluate the supplier's offer and state the maximum price Fenwick should pay for Q.
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Buying one Q at price X gives a net margin of £(45 − X), and frees 2 hours, which make 2/3 of a P earning 2/3 × £24 = £16 of contribution. Making Q in-house earns £21.
Indifference: (45 − X) + 16 = 21 → X = £40.00.
So £40 is the ceiling; above that, making Q is better. At the offered £38 each bought Q earns 45 − 38 + 16 = £23, i.e. £2 more than making it.
How many to buy? Two limits:
- Supplier capacity: 900 units
- Demand for P: extra P possible is 1,000 units (3,000 hrs), and 900 Q frees only 1,800 hrs = 600 P units, so P demand is not the binding limit
- Q demand: 3,500 made + 900 bought = 4,400 ≤ 4,500 ✓
Revised plan: buy 900 Q, make 2,600 P, 3,500 − 900... i.e. make 3,500 Q, 3,000 R and 2,600 P. Additional profit = 900 × £2 = £1,800, giving £39,300.
Note the answer is highly sensitive: at £41 per unit the offer destroys £1 per unit of value and should be refused outright.
3. What qualitative factors should Fenwick consider before accepting the supplier's offer?
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- Supplier reliability and quality. Buying in a product sold under Fenwick's own brand transfers quality and delivery risk to a third party. A late or faulty batch damages Fenwick's customers, not the supplier's reputation.
- Price risk. £38 may be an introductory price. Once in-house Q capacity has been stood down, the supplier has bargaining power and the £40 ceiling could be exceeded.
- Loss of capability. Reducing Q output by 900 units may erode learning, labour skills and overhead recovery; restarting later is costly.
- Workforce reaction. A buyer/supplier decision affecting shop-floor work can trigger industrial relations problems.
- Nature of P demand. The extra 600 P units are additional sales at full price - if that demand is uncertain or promotional, committing to bought-in Q to serve it is risky.
- Contract terms. Check whether the minimum P contract or customer agreements restrict mix changes, and whether the 900 bought-in units carry warranty obligations.
The financial case (£1,800 on £39,300 of profit) is thin enough that these factors could easily reverse the decision.