Compute profit and surge break‑even price

Q: Compute profit and surge break‑even price

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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Question

Context: You manage daily capacity and pricing for a ride‑share service. Each driver works an 8‑hour day and can complete at most 5 rides/hour (i.e., 40 rides/day). Drivers are hired for the full day only. Fixed cost is $10,000/day. Each driver is paid$ 700/day. Unless stated otherwise, all stated ride volumes must be fully served.

Single-price day

Demand: 2,400 rides/day priced at $30/ride.
Tasks: (a) How many drivers are required to serve demand without exceeding per‑driver caps? (b) What is the daily profit? Show algebra and verify feasibility (capacity ≥ demand).

Two-block day (4 hours non‑peak + 4 hours peak)

Non‑peak block: 800 rides at $30/ride.
Peak block: 1,600 rides at price P.
Constraints unchanged; drivers still hired for the full day.
Task: What peak price P yields exactly $0 daily profit (break even)? Provide the formula and numeric value. State any assumptions you make if capacity binds.

Compute profit and surge break‑even price

Solution

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Compute profit and surge break‑even price

Overview

Capacity and Break-even Pricing for a Ride-share Service

Solution

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