##### Scenario Onemain Financial must decide how to allocate marketing budget across three acquisition channels—Phone Calls, Social Media Ads, and Email Blasts—whose click-through rates, conversion rates, and revenue-per-cost values are provided in an Excel sheet. ##### Question Given a total budget B, calculate the expected net profit for each channel. 2. Using the conversion rate, estimate the average cost and the average profit generated by a single inbound phone call. 3. Each channel has an individual spend cap. With a fixed overall budget, determine the spending allocation that maximizes total profit and explain your reasoning. ##### Hints Compute unit profit (revenue – cost) first, then apply budget constraints and simple greedy/linear optimization to maximize profit.

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 Marketing 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 Take-home Project rounds at OneMain Financial.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at OneMain Financial during technical interviews.

Determine Optimal Marketing Budget Allocation for Maximum Profit

Budget Allocation Across Acquisition Channels

Context

You are given an Excel sheet with per-channel performance metrics for three acquisition channels: Phone Calls, Social Media Ads, and Email Blasts. For each channel, the sheet provides:

Click-through rate (CTR)
Conversion rate (CVR)
Revenue-per-cost (RPC), i.e., expected revenue generated per $1 of spend
An individual spend cap for that channel

If RPC is not directly provided, it can be derived from CTR, CVR, average revenue per conversion (R), and the channel's pricing model (e.g., CPM, CPC, cost per send). Assume linear returns up to each channel’s cap (no saturation within cap) and that all rates are stable over the budget range considered.

Tasks

Given a total budget B, compute the expected net profit for each channel if you allocate an amount s to that channel (you may consider the case where all of B is spent in a single channel, ignoring caps for this part).
Using the conversion rate for the Phone Calls channel, estimate:
- The average cost per inbound phone call
- The average profit per inbound phone call
Each channel has an individual spend cap. With a fixed overall budget B, determine the spending allocation across channels that maximizes total profit. Explain your reasoning.

Hints

First compute unit profit per $1 of spend for each channel: unit profit = revenue-per-cost − 1.
Then apply budget constraints and use a simple greedy/linear optimization to maximize profit under caps.

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?