A software company sells one seat per customer per month. Demand is q(p) = 10,000 − 50·p (units/month), variable cost c = $5 per seat, fixed monthly cost F = $100,000. 1) Derive the profit-maximizing price p* and quantity q* and compute the maximum monthly profit. Show your calculus. 2) If capacity is limited to 6,000 seats/month, what price maximizes profit under the constraint? 3) If a 10% price increase raises churn from 2% to 4% monthly (subscription setting), explain how your model changes and how you would estimate LTV-optimized price instead of static monthly profit.

This question evaluates pricing optimization, linear demand modeling, capacity-constrained profit maximization, and the impact of subscription churn on lifetime value within an Analytics & Experimentation data-science context.

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Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

What difficulty level is this interview question?

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

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

Optimize SaaS pricing and profit | OneMain Financial Interview Question

SaaS Pricing: Linear Demand, Capacity Constraint, and Subscription Churn

Context: You are pricing a single-seat SaaS product (one seat per customer per month). Demand for new seats in a given month follows a linear demand curve. Costs include a per-seat variable cost and a fixed monthly overhead.

Given:

Demand (new seats/month): q(p) = 10,000 − 50·p
Variable cost per seat: c = $5
Fixed monthly cost: F = $100,000

Tasks:

Unconstrained pricing: Derive the profit-maximizing price p* and quantity q*, and compute the resulting maximum monthly profit. Show your calculus.
Capacity constraint: If capacity is limited to 6,000 seats/month, what price maximizes profit under this constraint?
Subscription twist: In a subscription setting, a 10% price increase raises monthly churn from 2% to 4%. Explain how the model changes and how you would estimate an LTV-optimized price instead of a static monthly profit optimum.

SaaS Pricing: Linear Demand, Capacity Constraint, and Subscription Churn

Given:

Demand (new seats/month): q(p) = 10,000 − 50·p
Variable cost per seat: c = $5
Fixed monthly cost: F = $100,000

Tasks:

Unconstrained pricing: Derive the profit-maximizing price p* and quantity q*, and compute the resulting maximum monthly profit. Show your calculus.
Capacity constraint: If capacity is limited to 6,000 seats/month, what price maximizes profit under this constraint?
Subscription twist: In a subscription setting, a 10% price increase raises monthly churn from 2% to 4%. Explain how the model changes and how you would estimate an LTV-optimized price instead of a static monthly profit optimum.

Optimize SaaS pricing and profit

Quick Overview

SaaS Pricing: Linear Demand, Capacity Constraint, and Subscription Churn

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Optimize SaaS pricing and profit

Quick Overview

SaaS Pricing: Linear Demand, Capacity Constraint, and Subscription Churn

Solution

Comments (0)