Maintain target margin with fixed costs

Quick Overview

This question evaluates the ability to model profit margins by combining revenue, variable costs from a mixed-product portfolio, and fixed costs using algebraic manipulation and basic cost-accounting concepts for a Data Scientist role.

Maintain target margin with fixed costs

Company: Capital One

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Technical Screen

Target a 34.43% profit margin in Year 2. You will sell both products with the same prices as in Q4: classic price = $4, unit cost = $1; vegan price = $4, unit cost = $2; sales mix vegan:classic = 2:3. Year-2 fixed costs (independent of volume) are $375m. How many total burgers must you sell in Year 2 to achieve a 34.43% profit margin? Derive and solve for total units U using margin = (revenue − variable − fixed)/revenue.

Quick Answer: This question evaluates the ability to model profit margins by combining revenue, variable costs from a mixed-product portfolio, and fixed costs using algebraic manipulation and basic cost-accounting concepts for a Data Scientist role.

|Home/Statistics & Math/Capital One
Capital One logo
Capital One
Oct 13, 2025, 9:49 PM
mediumData ScientistTechnical ScreenStatistics & Math
3
0

Target Profit Margin With a Mixed-Product Portfolio

Context

You sell two burger products (classic and vegan) at the same price but with different unit costs. Year-2 fixed costs are known, and the sales mix between products is fixed. You want to find the total number of burgers to sell in Year 2 to achieve a target profit margin.

Given

  • Target profit margin (Year 2): 34.43% = 0.3443
  • Prices and unit costs:
    • Classic: price = 4,unitcost=4, unit cost = 1
    • Vegan: price = 4,unitcost=4, unit cost = 2
  • Sales mix (vegan : classic) = 2 : 3
  • Year-2 fixed costs (F) = $375,000,000

Task

Let U be the total number of burgers sold (all products combined). Using the definition

margin = (revenue − variable cost − fixed cost) / revenue,

derive and solve for U such that the margin equals 34.43%.

Loading comments...

Browse More Questions

More Statistics & Math•More Capital One•More Data Scientist•Capital One Data Scientist•Capital One Statistics & Math•Data Scientist Statistics & Math