Determine Weekly Break-Even Point for Diaper Service
Quick Overview
Evaluates unit economics and inventory flow for a diaper delivery and cleaning service. Strong answers calculate contribution margin and break-even customers, track unused diaper surplus, and propose stock-out levers.
Determine Weekly Break-Even Point for Diaper Service
Company: Capital One
Role: Data Scientist
Category: Analytics & Experimentation
Difficulty: medium
Interview Round: Onsite
##### Scenario
Subscription diaper-delivery & cleaning service: 350 babies; charge $20/baby/week; deliver 80 diapers per baby weekly; each baby uses 72 diapers/week; cleaning cost $0.05 per used diaper; delivery cost $10/baby/week; fixed overhead $1,040 per week.
##### Question
What is the weekly break-even point (expressed in number of babies served or weeks) for the business given the pricing and cost structure?
2) If deliveries begin on Monday, Jan 1, and diapers are collected, cleaned, and re-used weekly, how many unused diapers remain in inventory on the third Monday?
3) Suppose inventory is insufficient for scheduled deliveries in week 3. Suggest three operational levers the business could pull to avoid stock-outs.
##### Hints
Use contribution margin to find break-even; build a stock-flow timeline for inventory; think about capacity, collection frequency, and sourcing options.
Quick Answer: Evaluates unit economics and inventory flow for a diaper delivery and cleaning service. Strong answers calculate contribution margin and break-even customers, track unused diaper surplus, and propose stock-out levers.
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.
Constraints & Assumptions
Treat price, cleaning cost, delivery cost, and fixed overhead as weekly values.
State whether unused diapers stay with customers or are collected, and keep the accounting consistent.
Round customer break-even up to a whole number of babies.
Separate operating profit from inventory flow.
Clarifying Questions to Ask Guidance
Are unused clean diapers collected weekly or left with customers?
Is the service required to deliver exactly 80 diapers every Monday regardless of prior surplus?
Are lost, damaged, or unusable diapers ignored?
Is break-even being asked per week or cumulative over a launch period?
Part 1 - Weekly Break-even
Calculate the weekly break-even point in number of babies served. Also express the break-even timing at the current 350-baby scale.
What This Part Should Cover Guidance
Compute revenue per baby, variable cost per baby, and contribution margin.
Divide fixed overhead by contribution margin and round up to whole customers.
Compare fixed overhead against total weekly contribution at 350 babies.
Interpret the result clearly.
Part 2 - Unused Diapers on the Third Monday
If deliveries begin on Monday, Jan 1, and diapers are collected, cleaned, and reused weekly, calculate how many unused diapers are in the system on the third Monday.
What This Part Should Cover Guidance
Track the 8-diaper weekly surplus per baby from delivering 80 and using 72.
Make a minimal assumption about whether unused diapers are centralized or still with customers.
Multiply the per-baby unused surplus across 350 babies over the completed weeks.
Explain why location of unused diapers affects operations but not total unused inventory.
Part 3 - Operational Levers for Week-3 Stock-outs
If inventory is insufficient for scheduled deliveries in week 3, suggest three levers to avoid stock-outs.
What This Part Should Cover Guidance
Include levers such as adjusting delivery quantity, reclaiming clean surplus, accelerating collection, renting or buying temporary inventory, or changing delivery cadence.
Explain the operational trade-offs and customer-experience risks.
Add guardrails for service quality, hygiene, and safety stock.
Follow-up Questions Guidance
How would demand variability change the break-even and inventory plan?
What safety stock policy would you recommend?
How would you redesign the service to avoid accumulating unused diapers?
