Capital One·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Capital One data scientist case question that's basically a constrained optimization problem dressed up as a product/pricing scenario. Pretty math-heavy for what I expected from a DS interview.

Questions Asked (1)

You have a $150M content budget and each show costs $5M to produce. Using the WTP curve from a prior question, you price at the maximum willingness-to-pay implied by the number of shows, subject to a $20 price cap. How many shows do you produce and what monthly membership fee do you set? Then redo the calculation with a $250M total budget.

Pricing & MonetizationProduct StrategyProduct Analytics & Metrics

Author's notes

This one tripped me up because I kept second-guessing whether the $20 cap was binding or not.

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AI HintsAI Generated

Suggested Approach

First, clarify the WTP curve from the prior question (likely a linear or concave function relating number of shows to maximum willingness-to-pay). Then set up the optimization: maximize revenue (or profit) subject to budget and price cap, solving for the optimal number of shows and corresponding price. Repeat for the larger budget, noting how the optimal solution changes.

Pro tip: Always state your assumptions about the WTP curve explicitly, and show the marginal analysis: the optimal number of shows occurs where marginal revenue equals marginal cost (or where the budget constraint binds if the price cap is not binding).

1. Clarify the WTP curve and constraints

Restate the WTP curve from the prior question (e.g., P = a - bQ or a table) and note the $20 price cap and budget constraints. Confirm units and that each show costs $5M.

2. Set up the optimization problem

Define the decision variable Q (number of shows). The budget constraint is 5Q ≤ B (B = 150 or 250). The price is P = min(WTP(Q), 20). Revenue is P * Q (or profit if costs are considered).

3. Solve for optimal Q and P under $150M budget

Maximize revenue subject to 5Q ≤ 150 and P ≤ 20. Check if the unconstrained optimal Q (where marginal revenue = 0) is feasible; if not, the budget binds. Compute P from the WTP curve and apply the cap if needed.

4. Repeat for $250M budget

Redo the optimization with B = 250. Compare the new optimal Q and P to the previous case, noting the effect of the larger budget.

5. Interpret and sanity-check results

Ensure Q is an integer (if shows are discrete), P is within the cap, and the budget is not exceeded. Discuss how the price cap may or may not bind depending on Q.

Key Points to Mention

The WTP curve from the prior question (e.g., linear demand P = a - bQ) and its parameters.
Budget constraint: total cost = 5Q ≤ B, so Q ≤ B/5.
Price cap: P ≤ 20, so if WTP(Q) > 20, set P = 20.
Revenue maximization: find Q where marginal revenue = 0 (if unconstrained) or where budget binds.
For B=150, Q_max = 30; for B=250, Q_max = 50. Check if optimal Q is less than these.
The effect of the price cap: if the cap binds, increasing Q may not increase revenue beyond a point.

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