Make-or-buy with a constrained resource
Bramwell Components makes three parts. Per-unit data: Part A sells for $40, variable cost $22, uses 2 machine hours. Part B sells for $55, variable cost $37, uses 3 machine hours. Part C sells for $30, variable cost $15, uses 1.5 machine hours. Fixed costs are $180,000 per year and machine capacity is 24,000 hours. Current demand: 3,000 A, 2,500 B, 4,000 C. A supplier offers Part B at $34 per unit delivered. Bramwell's accountant says B should be bought in because $34 is below the $55 selling price. The production manager warns that spare capacity does not exist.
1. Calculate the contribution per machine hour for each part and determine the optimal production plan given the capacity constraint.
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Contribution per unit and per machine hour:
| Part | Price | Var cost | Contribution | Hours | Contribution/hour |
|---|---|---|---|---|---|
| A | $40 | $22 | $18 | 2.0 | $9.00 |
| B | $55 | $37 | $18 | 3.0 | $6.00 |
| C | $30 | $15 | $15 | 1.5 | $10.00 |
Ranking: C ($10.00) > A ($9.00) > B ($6.00).
Hours needed for full demand: A 6,000 + B 7,500 + C 6,000 = 19,500 hours - within the 24,000-hour capacity. So on these figures all demand can be met and there is 4,500 hours spare.
The accountant's reasoning is still wrong in principle: comparing a buy price to a selling price ignores the variable cost saved. The relevant comparison is the buy price ($34) against the avoidable cost of making B ($37 variable), giving a $3 per-unit saving from buying - before considering what the freed 3 hours per unit could earn. Buying B frees 7,500 hours, which at the next-best use (A, $9/hour) could generate $67,500 of contribution, far exceeding the $7,500 saving on B's variable cost.
2. Advise whether Bramwell should accept the supplier offer, quantifying the opportunity cost. State two qualitative factors.
Read the worked answer
If B is bought in:
- Saving on B: 2,500 × ($37 − $34) = $7,500
- Hours freed: 2,500 × 3 = 7,500 hours
- Best alternative use: Part A at $9.00 contribution/hour = 7,500 × $9 = $67,500
- Net advantage of buying B and expanding A = $7,500 + $67,500 = $75,000
But check feasibility: A demand is 3,000 units (6,000 hours). The freed 7,500 hours exceeds A's remaining demand. If A can only absorb 6,000 hours (3,000 units), contribution from A = $54,000, and the remaining 1,500 hours go to C at $10/hour = $15,000. Total = $7,500 + $54,000 + $15,000 = $76,500 - but only if A and C demand can actually be sold. Market demand caps the benefit.
Recommendation: accept the offer only if the additional A and C units can be sold. If demand is fixed at current levels, buying B yields just $7,500 and introduces supply risk for modest gain.
Qualitative factors: (1) supplier reliability and quality - a late or faulty delivery stops Bramwell's own production; (2) loss of in-house skills and future bargaining power if the supplier later raises prices; also consider redundancy costs and the strategic value of the B product line.