Calculate tiered cost and break-even
Company: MathWorks
Role: Software Engineer
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
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.