Determine Optimal Budget Allocation for Maximum Profit

Quick Overview

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.

Determine Optimal Budget Allocation for Maximum Profit

Company: Capital One

Role: Data Scientist

Category: Analytics & Experimentation

Difficulty: medium

Interview Round: Technical Screen

##### 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.

Quick Answer: 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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Aug 4, 2025, 10:55 AM
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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

  1. If you allocate the entire budget B to a single platform i, compute its expected net profit.
  2. 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.
  3. 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.

Clarifying Questions to Ask Guidance

  • 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 Guidance

  • 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 Guidance

  • 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?
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