Compute capacity, staffing trade-offs, and break-even

Capacity, Cost, and Staffing Planning for a 2‑Week Sprint

Context

• You manage a 3‑person dev‑tools team. Each line of code must be coded, tested, and documented within the same 2‑week sprint. Work proceeds simultaneously by role; overall throughput is constrained by the slowest role (the bottleneck).
• Roles (one person each), base pay $16/hour, 40 hours/week, 2 weeks/sprint → 80 hours/person/sprint. Base wages are paid regardless of utilization.
• Overtime (OT) is $24/hour and applies only to hours beyond 40 hours/week (i.e., beyond 80 hours per sprint).
• A contractor Coder is available only full‑time (40 hours/week → 80 hours/sprint) at $24/hour.
• Current realized output: 1,000 lines per sprint.

Productivity

• Coder: 15 lines/hour
• Tester: 2 lines per 5 minutes = 24 lines/hour
• Documenter: 1 line per 2 minutes = 30 lines/hour

Tasks

1. Compute the team’s maximum two‑week capacity under the simultaneous‑work assumption and identify the bottleneck. Can 2,000 lines be met without overtime or hiring?
2. If taking the customer (target 2,000 lines/sprint), compare two strategies:
   • A) Use only overtime for existing staff.
   • B) Hire one full‑time contractor Coder and use overtime for any remaining role if needed. For each, calculate total labor cost per sprint, split into base vs overtime/contract, and choose the cheaper option.
3. Under the cheaper option from (2), compute the break‑even revenue per line at 1,000 lines and at 2,000 lines per sprint (revenue per line such that profit = 0 given base wages plus any overtime/contract expense).
4. Quantitatively explain why the break‑even per line at 2,000 lines should be lower than at 1,000.
5. Recommend short‑term and long‑term staffing if demand may fluctuate ±20% around 2,000 lines for the next two quarters; justify using the bottleneck and sensitivity analysis.