Determine Weekly Break-Even Point for Diaper Service
Overview
This question evaluates unit-economics, inventory flow, and basic financial modeling skills relevant to pricing, break-even analysis, and capacity planning for a subscription-based operational service.
Capital One
Jul 12, 2025, 6:59 PM
Data Scientist
Onsite
Analytics & Experimentation
56
0
Diaper Service Unit Economics and Inventory Flow
Scenario
A weekly subscription diaper-delivery and cleaning service operates with these parameters:
- Customers: 350 babies
- Price: $20 per baby per week
- Delivery: 80 diapers per baby delivered each Monday
- Usage: Each baby uses 72 diapers per week (on average)
- Cleaning cost: $0.05 per used diaper
- Delivery cost: $10 per baby per week
- Fixed overhead: $1,040 per week
Assume weekly operations follow a Monday cycle: collect last week's diapers, clean, and deliver for the coming week. Unless stated otherwise, deliveries are a fixed 80 diapers per baby each week.
Questions
- What is the weekly break-even point (expressed in number of babies served, and alternatively in weeks at the current 350-baby scale) given the pricing and cost structure?
- If deliveries begin on Monday, Jan 1, and diapers are collected, cleaned, and re-used weekly, how many unused diapers are in the system on the third Monday? State any minimal assumptions you make about what gets collected.
- Suppose inventory is insufficient for scheduled deliveries in week 3. Suggest three operational levers the business could pull to avoid stock-outs.
Solution
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