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

You manage an e‑commerce dev‑tools team with three simultaneous roles paid $16/hour each: Coder (15 lines/hour), Tester (2 lines per 5 minutes), and Documenter (1 line per 2 minutes). A sprint is two weeks (40 hours/week/person). Current output is 1,000 lines per two weeks. A potential customer requires an additional 1,000 lines every two weeks (target 2,000 lines/sprint). A contractor Coder is available at $24/hour but must be hired full‑time (40 hours/week). Overtime for existing staff is paid at 1.5× ($24/hour) only for hours beyond 40/week. Assume base wages for the three existing roles (80 hours each per sprint) are paid regardless of utilization. Answer: 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, compare two strategies to reach 2,000 lines: A) use only overtime; B) hire one full‑time contractor Coder and use overtime for any remaining role if needed. For each, calculate total labor cost per two‑week sprint (split into base vs overtime/contract) and choose the cheaper option. 3) Under the cheaper option, compute the break‑even revenue per line for 1,000 lines and for 2,000 lines per sprint (i.e., revenue per line that yields zero profit 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 given demand may fluctuate ±20% around 2,000 lines for the next two quarters; justify using bottleneck and sensitivity analysis.