Compute profit and surge break‑even price

A ride-hailing platform handles 2,400 trips per day at a fixed fare of $30 per trip. Each driver earns $700 for the day, the workday lasts 8 hours, and no driver can take more than 5 rides per hour. Daily fixed costs are $10,000. Drivers must be hired for the entire day.

Answer the following:

1. How many drivers are needed to meet demand while staying within the per-driver ride limit, and what is the resulting daily profit? Show your calculations and confirm that available capacity is at least equal to demand.
2. Suppose the day is divided into two 4-hour periods: the non-peak block has 800 rides at $30 each, while the peak block has 1,600 rides at price P. Costs and driver limits stay the same, and drivers are still hired for the full day. What value of P makes daily profit exactly $0 (break even)? Give the formula and the numeric result, and note any assumptions you make if capacity becomes binding.

Overview: This question tests capacity planning and profit modeling, particularly how to work with discrete service limits, fixed and variable costs, and break-even pricing. It is frequently used because it measures applied quantitative reasoning and operational trade-off analysis; under Statistics & Math, it emphasizes real-world application over purely theoretical concepts.