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Cyclic Inequality in 4 variables with abcd=1

Source: MEMO Team Competition, Question 5

September 24, 2007
inequalitiesinequalities proposed

Problem Statement

Let a,b,c,d a,b,c,d be real numbers which satisfy 12≤a,b,c,d≤2 \frac{1}{2}\leq a,b,c,d\leq 2 and abcd\equal{}1. Find the maximum value of \left(a\plus{}\frac{1}{b}\right)\left(b\plus{}\frac{1}{c}\right)\left(c\plus{}\frac{1}{d}\right)\left(d\plus{}\frac{1}{a}\right).
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