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Maximum value of sum of fractions

Source: Centroamerican Olympiad 2014, problem 3

June 10, 2014
inequalitiesinequalities proposed

Problem Statement

Let aa, bb, cc and dd be real numbers such that no two of them are equal,
ab+bc+cd+da=4\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=4 and ac=bdac=bd. Find the maximum possible value of
ac+bd+ca+db.\frac{a}{c}+\frac{b}{d}+\frac{c}{a}+\frac{d}{b}.
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