Compute profit and surge break‑even price
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
A ride‑share service gives 2,400 rides/day at a flat $30/ride. Each driver is paid $700/day, days are 8 hours long, and a driver can complete at most 5 rides/hour. Fixed cost is $10,000/day. You must hire drivers for the full day. Answer: 1) How many drivers are required to serve demand without exceeding the per‑driver cap, and what is the daily profit? Show the algebra and verify feasibility (capacity ≥ demand). 2) Now the day splits into two 4‑hour blocks: non‑peak has 800 rides priced at $30; peak has 1,600 rides priced at P. Costs and driver constraints are unchanged, and drivers are still hired for the full day. What peak price P yields exactly $0 daily profit (i.e., break even)? Provide the formula and numeric value, and state any assumptions you make if capacity binds.
Overview: This question evaluates capacity planning and profit-modeling skills, focusing on handling discrete service caps, fixed and variable costs, and break-even pricing. It is commonly asked because it assesses applied quantitative reasoning and operational trade-off analysis; categorized under Statistics & Math, it tests practical application rather than purely theoretical concepts.
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