##### Scenario You are given performance metrics for three acquisition platforms—live phone calls, social-media ads, and email campaigns—and a fixed marketing budget. ##### Question With total budget B, cost-per-acquisition (CPA) and revenue-per-acquisition (RPA) for each platform, compute the expected net profit for every platform. 2. Using click-through and conversion rates, estimate the average cost incurred and profit earned from a single inbound phone call. 3. Each platform has a maximum spend cap. Given the same budget B, determine the optimal budget allocation across platforms to maximize overall profit. ##### Hints Units purchased = budget/CPA; profit = units × (RPA − CPA). For allocation, rank by unit profit, fund highest until its cap, then move to the next.

This interview question evaluates metric design, causal reasoning, experiment setup, diagnostics, SQL/statistical checks, and recommendations in a realistic interview setting. A strong answer for Determine Optimal Budget Allocation for Maximum Profit states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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What difficulty level is this interview question?

This is a medium difficulty Analytics & Experimentation question, commonly asked during Technical Screen rounds at Capital One.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Determine Optimal Budget Allocation for Maximum Profit

Scenario

You have three user-acquisition platforms: Live Phone Calls, Social Media Ads, and Email Campaigns. You are given a total marketing budget B. For each platform i, you know its cost per acquisition (CPA_i) and revenue per acquisition (RPA_i). Each platform also has a maximum spend cap Cap_i.

Additionally, you have funnel metrics for the Live Phone Calls channel: click-through rate (CTR), click-to-call rate (q_call|click), and call-to-purchase (acquisition) rate (q_acq|call). Media buying cost may be given as cost per click (CPC) or cost per thousand impressions (CPM).

Assumptions (explicit):

CPAs and RPAs are average marginal values and remain constant within the relevant spend ranges (no diminishing returns within caps).
Budget is divisible (fractional expected acquisitions are acceptable).
For the phone-call funnel, if CPC is not given but CPM is, use CTR to derive CPC.

Questions

If you allocate the entire budget B to a single platform i, compute its expected net profit.
Using click-through and conversion rates for the Live Phone Calls funnel, estimate the average marketing cost incurred and expected profit earned from a single inbound phone call.
Each platform has a maximum spend cap. Given the same budget B and caps Cap_i, determine the optimal allocation across platforms to maximize total profit.

Hints

Units acquired = budget / CPA.
Profit = units × (RPA − CPA).
For allocation with caps, rank platforms by profit per dollar of spend and fund greedily until caps or budget are exhausted.

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.
If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask

Clarify the business objective, unit of analysis, time window, exposure definition, and primary metric.
State assumptions about instrumentation, randomization, sample size, and data quality.
Separate descriptive analysis from causal claims.

What a Strong Answer Covers

A metric framework with primary, guardrail, and diagnostic metrics.
A credible analysis or experiment design with clear assumptions and bias checks.
SQL/statistical logic for segmentation, variance, confidence, and data validation where relevant.
An actionable recommendation that explains trade-offs and next steps.

Follow-up Questions

What sanity checks would you run before trusting the result?
How would you handle novelty effects, seasonality, or selection bias?
What decision would you make if metrics disagree?