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TL;DR

AM-GM for Constrained Optimization: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, HRT, Optiver.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateReal Analysis & Inequalities

AM-GM for Constrained Optimization

Asked at: Jane Street, HRT, Optiver

Problem
Without calculus, find the maximum value of f(x,y,z)=xyzf(x, y, z) = xyz subject to x+y+z=12x + y + z = 12 and x,y,z>0x, y, z > 0. Then find the minimum of \ racab+\ racbc+\ racca\ rac{a}{b} + \ rac{b}{c} + \ rac{c}{a} for positive reals a,b,ca, b, c.
Related concepts
Am Gm InequalityOptimization

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