Capital One·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Capital One data scientist interview with a case question that was more math-heavy than I expected. One question, but it had a lot of moving parts and I definitely fumbled the edge case interpretation.

Questions Asked (1)

A restaurant is considering adding a Vegan burger to its menu. The Regular burger earns $3 margin per unit, the Vegan earns $2. There are fixed costs F for launching the Vegan option (staff training, supplier fees), and a cannibalization rate c representing the share of Vegan sales that come from customers who would have otherwise bought a Regular. Derive the minimum Vegan unit sales needed to break even on profit, interpret what happens when c equals 0 or 1, and explain how you'd estimate c in practice.

Pricing & MonetizationProduct Analytics & MetricsA/B Testing & Experimentation

Author's notes

I got the algebra right but stumbled explaining the edge cases out loud.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by setting up the profit equation: incremental profit = Vegan units * (Vegan margin - cannibalized Regular margin) - fixed costs. Solve for the break-even quantity, then analyze the extreme cases c=0 and c=1 to build intuition. Finally, discuss practical methods to estimate c, such as A/B testing or customer surveys, and emphasize the importance of validating assumptions.

Pro tip: Frame the break-even quantity as a function of c and highlight that as c approaches 1, the required sales may become infinite if the net margin per Vegan unit is zero or negative. This shows you understand the business risk of cannibalization.

1. Define the profit equation

Let Q be the number of Vegan burgers sold. The incremental profit from adding the Vegan burger is: Profit = Q * (2 - c*3) - F. This accounts for the $2 margin per Vegan and the lost $3 margin on each cannibalized Regular sale.

2. Solve for break-even Q

Set Profit = 0 and solve for Q: Q = F / (2 - 3c). This is the minimum Vegan unit sales needed to cover fixed costs and cannibalization losses.

3. Interpret extreme cases

When c=0, Q = F/2 (no cannibalization, break-even at F/2 units). When c=1, Q = F/(2-3) = -F, which is impossible; this means if every Vegan sale cannibalizes a Regular sale, the net margin per Vegan is -$1, so you can never break even—you lose money on each sale.

4. Explain estimation of c

In practice, estimate c via A/B testing (e.g., introduce Vegan in test markets and compare Regular sales to control), customer surveys, or analyzing purchase patterns with loyalty data. Consider that c may vary by segment and over time.

5. Discuss assumptions and limitations

Acknowledge that the model assumes constant margins and linear cannibalization, and that fixed costs are truly fixed. Sensitivity analysis around c and F can help assess risk.

Key Points to Mention

Break-even formula: Q = F / (2 - 3c)
Cannibalization reduces effective margin per Vegan unit
c=0: no cannibalization, break-even at F/2 units
c=1: net margin negative, break-even impossible (Q negative)
Estimating c via A/B tests or customer surveys
Sensitivity analysis and assumptions (constant margins, linear cannibalization)

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.