The Overtime Budget Squeeze
A regional logistics firm has a monthly labour budget of $48,000 for its warehouse. The warehouse runs 22 working days per month. Currently it employs 30 workers at a fixed daily rate of $60 each, regardless of hours worked. Last month, the firm recorded 1,540 overtime hours, paid at a premium of $18 per hour on top of the fixed daily rate. Management forecasts that next month's shipment volume will rise by 12%, and that overtime hours scale proportionally with volume unless new workers are hired. Each new hire costs the same $60/day and reduces the overtime pool by 40 hours per month (because the work is redistributed). A new hire also carries a one-time recruitment cost of $450. The firm cannot exceed the $48,000 monthly labour budget and cannot hire more than 6 workers.
1. Determine the maximum number of new hires the firm can afford next month while staying within budget, and state whether that number is sufficient to bring overtime to zero.
Read the worked answer
Step 1 - Baseline overtime next month. Current overtime = 1,540 hours. With a 12% volume rise and no hires: 1,540 × 1.12 = 1,724.8 hours.
Step 2 - Baseline cost. Fixed wages = 30 × $60 × 22 = $39,600. Overtime = 1,724.8 × $18 = $31,046.4. Total = $70,646.4, far above $48,000. So hiring is mandatory.
Step 3 - Cost with n hires. Fixed wages = (30 + n) × 60 × 22 = 39,600 + 1,320n. Overtime hours = 1,724.8 − 40n. Overtime cost = 18(1,724.8 − 40n) = 31,046.4 − 720n. Recruitment = 450n. Total = 39,600 + 1,320n + 31,046.4 − 720n + 450n = 70,646.4 + 1,050n.
Step 4 - Interpret. The coefficient on n is positive: every hire adds $1,050 net. Hiring cannot rescue the budget - the firm is structurally over budget. Even n = 0 is over $48,000.
Conclusion: No number of hires (0–6) fits the budget; the maximum affordable is 0, and overtime cannot be eliminated by hiring alone. The fixed-rate wage structure, not headcount, is the binding constraint. A correct answer must flag that the budget is infeasible under current assumptions rather than force a hire count.
2. Management proposes cutting the overtime premium from $18 to $12 per hour instead of hiring. Evaluate whether this alone closes the budget gap, and identify the hidden assumption in the proposal.
Read the worked answer
Recompute at $12/hr, no hires. Overtime cost = 1,724.8 × 12 = $20,697.6. Fixed = $39,600. Total = $60,297.6. Still $12,297.6 over budget.
With 6 hires at $12/hr: Fixed = 39,600 + 1,320×6 = $47,520. Overtime hours = 1,724.8 − 240 = 1,484.8 → cost = $17,817.6. Recruitment = $2,700. Total = $68,037.6. Worse than no hires because the fixed-wage term dominates.
Conclusion: The premium cut alone does not close the gap ($60,298 > $48,000).
Hidden assumption: The proposal assumes overtime hours are fixed and only the rate matters. In reality, lowering the premium may reduce the incentive for workers to volunteer for overtime, potentially increasing the need for hires or reducing throughput. The model also assumes volume growth is unavoidable - if the 12% forecast is soft, deferring volume is a cheaper lever than either option. A strong answer names the volume assumption as the real variable to challenge.