Calculate tiered cost and break-even

Quick Overview

This question evaluates the ability to model tiered piecewise cost functions, compute total and average unit costs, and perform break-even analysis using basic algebra and arithmetic.

Calculate tiered cost and break-even

Company: MathWorks

Role: Software Engineer

Category: Statistics & Math

Difficulty: medium

Interview Round: Online Assessment

A vendor charges a fixed setup fee of $500 per order. The unit price is $12 for the first 1,000 units and $9 for each additional unit beyond 1,000. Shipping costs $0.80 per unit for the first 2,000 units and $0.50 for each unit thereafter. (a) Write a formula for total cost as a function of quantity q. (b) Compute total and average cost per unit for q = 1,600 and q = 3,200. (c) If your resale price is $15 per unit, what is the break-even quantity? Show steps.

Quick Answer: This question evaluates the ability to model tiered piecewise cost functions, compute total and average unit costs, and perform break-even analysis using basic algebra and arithmetic.

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Aug 10, 2025, 12:00 AM
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Tiered Pricing and Shipping Cost Function

You are ordering q units from a vendor with the following pricing:

  • Fixed setup fee per order: $500
  • Unit price: 12forthefirst1,000units;12 for the first 1,000 units; 9 for each additional unit beyond 1,000
  • Shipping: 0.80perunitforthefirst2,000units;0.80 per unit for the first 2,000 units; 0.50 per unit thereafter

Tasks: (a) Write a formula for the total cost C(q) as a function of quantity q. (b) Compute the total and average cost per unit for q = 1,600 and q = 3,200. (c) If your resale price is $15 per unit, find the break-even quantity. Show your steps.

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