Make-or-Buy with a Binding Constraint
Jeddah Foods produces three products. Machine hours are the binding constraint: 40,000 hours available per month. Product data per unit: A - contribution SAR 30, 3 machine hours, demand 6,000 units; B - contribution SAR 24, 2 machine hours, demand 8,000 units; C - contribution SAR 18, 1.5 machine hours, demand 10,000 units. Fixed costs are SAR 500,000 per month and are unavoidable. A supplier has offered to supply Product C at SAR 26 per unit, while Jeddah Foods' variable cost of C is SAR 20 per unit (selling price is SAR 38). The production manager proposes dropping C to free capacity for A and B, which he says are 'more profitable per unit'.
1. Rank the products and determine the optimal production plan.
Read the worked answer
Rank by contribution per machine hour (the scarce resource), not per unit:
| Product | Contribution/unit | Hours/unit | Contribution per hour | Rank |
|---|---|---|---|---|
| A | 30 | 3.0 | 10.00 | 1 |
| B | 24 | 2.0 | 12.00 | 1 (highest) |
| C | 18 | 1.5 | 12.00 | 1 (tied with B) |
Recalculating: A = 10.00; B = 12.00; C = 12.00. So B and C tie for first, A is last. The production manager's 'per unit' reasoning is wrong - A has the highest contribution per unit but the lowest per hour.
Optimal plan (fill highest contribution per hour first):
- B: 8,000 × 2 = 16,000 hours; contribution 8,000 × 24 = SAR 192,000
- C: 10,000 × 1.5 = 15,000 hours; contribution 10,000 × 18 = SAR 180,000
- Hours used = 31,000; remaining = 9,000 hours
- A: 9,000 / 3 = 3,000 units; contribution 3,000 × 30 = SAR 90,000
Total contribution = SAR 462,000; profit after fixed costs = 462,000 − 500,000 = (SAR 38,000) loss.
Note: A is only produced because spare capacity remains after satisfying full demand for B and C.
2. Evaluate the buy option for Product C and advise whether to accept the supplier's offer.
Read the worked answer
Relevant cost of making C = variable cost SAR 20/unit. The SAR 26 offer is SAR 6 higher per unit on the face of it, but the decision must account for the opportunity cost of the 1.5 machine hours released.
If C is bought out:
- Extra purchase cost: 10,000 × (26 − 20) = SAR 60,000 increase
- Capacity released: 15,000 hours, which can be used for Product A at SAR 10 contribution per hour
- Contribution gained from A: 15,000 × 10 = SAR 150,000
- Net benefit of buying C = 150,000 − 60,000 = SAR 90,000
Revised plan if C is bought: B (16,000 hrs) + A up to demand 6,000 × 3 = 18,000 hrs = 34,000 hrs, within 40,000.
- Contribution: B 192,000 + A 180,000 = SAR 372,000, less the incremental buy cost of 60,000 → SAR 312,000...
Careful: compare like with like. Make-and-sell plan contribution was SAR 462,000. Buy-C plan: contribution from A and B = 372,000, and C is resold at selling price 38 − purchase 26 = SAR 12 contribution × 10,000 = 120,000 → total SAR 492,000. That is SAR 30,000 better than making.
Advice: accept the offer, provided quality, delivery reliability and the supplier's capacity are assured, and provided the released capacity can genuinely be sold (demand for A is only 6,000 units). Qualitative factors: loss of control over quality, dependency on a single supplier, workforce implications, and whether the SAR 26 price is sustainable beyond the contract term.