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Determine Optimal Budget Allocation for Maximum Profit

Capital OneData Scientist · Technical Screen
MediumData ScientistTechnical ScreenAnalytics & Experimentation

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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.

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.