Halversen Optics: Mix Under a Contract Constraint
Halversen Optics makes two lens types on one grinding cell that runs 8,000 machine hours a year; changeovers consume 96 hours of that. Standard lens: price $60, variable cost $42, 0.5 machine hours, annual demand 12,000 units. Precision lens: price $120, variable cost $75, 1.5 machine hours, annual demand 4,000 units. A hospital group contract requires Halversen to supply at least 2,500 precision lenses a year; below that the group moves all of its business, including 3,000 standard lenses, to a rival. Fixed costs are $180,000 a year and are unaffected by mix. A distributor has offered to buy 1,000 precision lenses at $100 each. Separately, a neighbouring plant has 1,000 spare machine hours it will lease for $20,000 a year.
1. Determine the optimal product mix that honours the contract and quantify what the contract constraint costs in contribution.
Read the worked answer
Rank by contribution per machine hour, not per unit
| Standard | Precision | |
|---|---|---|
| Price | 60 | 120 |
| Variable cost | 42 | 75 |
| Contribution/unit | 18 | 45 |
| Hours/unit | 0.5 | 1.5 |
| Contribution/hour | $36 | $30 |
Standard earns more per scarce hour, so fill standard demand first - unless constrained otherwise.
Hours available: 8,000 − 96 changeover = 7,904.
Mix with the contract (the feasible optimum) Precision 2,500 × 1.5 = 3,750 hours. Remaining 4,154 hours ÷ 0.5 = 8,308 standard units. Contribution = 2,500 × 45 + 8,308 × 18 = 112,500 + 149,544 = $262,044.
Mix without the contract (the theoretical optimum) Standard 12,000 × 0.5 = 6,000 hours. Remaining 1,904 ÷ 1.5 = 1,269 precision units. Contribution = 216,000 + 57,105 = $273,105.
Cost of the constraint = $11,061 of contribution a year - the price of keeping the account.
Why it is still the right call: standard demand (12,000) exceeds what the cell can supply (8,308) in either scenario, so losing the group's 3,000 standard lenses costs nothing in the short run - the value of the contract is purely relational and reputational. That is a strategic judgement, not a costing one, and should be stated as such: a saving of $11k against the risk of a reputational loss in a referral-driven hospital market is a cheap insurance premium, provided the customer is not treated as a captive and premium-priced against.
2. Should Halversen accept the distributor's offer of 1,000 precision lenses at $100?
Read the worked answer
Naive answer (wrong): $100 − $75 = $25 contribution per unit, positive, so accept. That treats scarce capacity as free.
Correct test: contribution per constrained hour versus the alternative use.
- Order contribution: $25 × 1,000 = $25,000.
- Hours consumed: 1,000 × 1.5 = 1,500 hours.
- Alternative use: those hours make 1,500 ÷ 0.5 = 3,000 standard lenses at $18 = $54,000.
Net effect of accepting = 25,000 − 54,000 = −$29,000. Reject at $100.
Break-even price: the order must return $36 per hour, so required contribution per unit = 36 × 1.5 = $54, i.e. a price of 75 + 54 = $129. The distributor's $100 is $29 a unit short.
Caveats that would change the answer:
- If standard demand were fully satisfied and hours were idle, any contribution above variable cost would be worth taking (with a watch on price erosion and on setting a precedent for the $129 list).
- If the order were a one-off market-entry trial with option value, that would be a strategic investment argued on its own merits, not a costing decision.
- If fixed costs were genuinely avoidable, they would enter the analysis.
Since standard demand is 3,692 units unmet, there is no idle capacity and the order fails cleanly.
3. Evaluate the offer to lease 1,000 machine hours for $20,000 a year, and note any qualitative issues.
Read the worked answer
Value of an incremental hour = the contribution of the best alternative use = standard lens at $36/hour (unmet standard demand of 3,692 units = 1,846 hours, so 1,000 hours can all be absorbed).
- Contribution gained: 1,000 × 36 = $36,000
- Cost: $20,000
- Net gain: $16,000 a year - accept, on the numbers.
Alternatively framed: 2,000 extra standard units × $18 = $36,000 vs $20,000, a $16,000 gain, or $8 per unit of extra output.
Qualitative and risk tests before signing:
- Quality and capability: can the neighbouring plant hold lens tolerances? Scrap and rework on precision optics can erase $16,000 quickly; a trial batch with agreed quality gates is prudent.
- Term and reliability: a one-year lease on a bottleneck that is being used opportunistically creates dependency - price will be renegotiated upward once Halversen has committed customers to the output.
- Duration vs the real fix: leasing buys throughput but does not relieve the underlying constraint. The higher-value structural moves are reducing the 96 changeover hours (every hour saved is worth $36) and attacking precision setup time, which is what makes precision expensive per hour.
- Effect on the contract: extra standard capacity does not help the hospital group, whose constraint is precision hours - the lease improves profit but not the strategic problem.
Recommendation: take the lease subject to a quality trial and a renewal price cap; run a changeover-reduction project in parallel.