Capital One·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Capital One data scientist interview with a multi-part burger profitability case. The math gets layered fast once you introduce a second product line with its own cost structure, and they want both the formula and the number.

Questions Asked (1)

In Year 2, a Vegan burger option is added with fixed costs of $60m/year in training and $2.25m/month in supplier costs. Prices and variable costs stay the same (Regular: $4 price, $1 cost; Vegan: $4 price, $2 cost), and the sales mix is Vegan to Regular at 2:3. What total number of burgers do you need to sell in Year 2 to maintain the same profit margin as Year 1? Give both the general formula and the final number.

Pricing & MonetizationProduct Analytics & Metrics

Author's notes

This one is where I started second-guessing myself.

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AI HintsAI Generated

Suggested Approach

First, calculate Year 1 profit and profit margin using the given Regular burger price and cost. Then, for Year 2, express total profit as a function of total quantity Q, incorporating the new Vegan burger's fixed and variable costs and the sales mix. Set Year 2 profit margin equal to Year 1 margin and solve for Q.

Pro tip: Clearly state your assumptions about Year 1 sales volume and whether fixed costs are annual or monthly, as the question may be ambiguous. If Year 1 volume is not provided, you can derive the required Q in terms of Year 1 volume or assume a base volume (e.g., 100 burgers) to illustrate the calculation.

1. Compute Year 1 Profit Margin

Calculate the profit per Regular burger (price - variable cost) and the profit margin (profit per burger / price). Since only Regular burgers are sold in Year 1, the margin is (4 - 1)/4 = 0.75 or 75%.

2. Determine Year 2 Fixed Costs

Sum the annual fixed costs: training $60m/year plus supplier costs $2.25m/month * 12 = $27m/year, totaling $87m/year.

3. Express Year 2 Profit as a Function of Q

With a Vegan to Regular sales mix of 2:3, Vegan burgers = (2/5)Q and Regular = (3/5)Q. Total revenue = 4Q. Total variable cost = 2*(2/5)Q + 1*(3/5)Q = (7/5)Q. Profit = 4Q - (7/5)Q - 87m = (13/5)Q - 87m.

4. Set Profit Margin Equal to Year 1 and Solve for Q

Year 2 profit margin = Profit / Revenue = [(13/5)Q - 87m] / (4Q) = 0.75. Solve: (13/5)Q - 87m = 3Q => (13/5 - 15/5)Q = 87m => (-2/5)Q = 87m => Q = -217.5m, which is impossible. This indicates an error; re-evaluate the margin definition or assumptions.

5. Re-evaluate and Correct the Approach

Recognize that with the given costs, the Year 2 profit margin is always less than 75% for any positive Q. To maintain the same profit margin, the fixed costs must be covered by additional profit, but the margin cannot be maintained. Thus, the question may intend to maintain the same total profit, not margin. If maintaining total profit, set Year 2 profit equal to Year 1 profit (which depends on Year 1 volume). Without Year 1 volume, express Q in terms of Year 1 volume or assume a value.

Key Points to Mention

Profit margin definition: profit divided by revenue.
Year 1 profit margin calculation: (4-1)/4 = 75%.
Year 2 fixed costs: $60m training + $2.25m*12 supplier = $87m.
Sales mix: Vegan:Regular = 2:3, so Vegan = 2/5 Q, Regular = 3/5 Q.
Year 2 profit equation: Profit = 4Q - (2*(2/5)Q + 1*(3/5)Q) - 87m = (13/5)Q - 87m.
Setting margin equal to 75% leads to negative Q, indicating impossibility; clarify if the goal is to maintain total profit instead.

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