Let
![a,b,c,d](/media/m/7/6/0/7605ede133e1f767d3890e0bfffb7b7f.png)
be real numbers which satisfy
![\frac{1}{2}\leq a,b,c,d\leq 2](/media/m/c/5/9/c59d5d095ef229c34259a5dd46a83a8b.png)
and
![abcd=1](/media/m/a/2/b/a2bb57b78cfba6434c7eb6534e0383ff.png)
. Find the maximum value of
%V0
Let $a,b,c,d$ be real numbers which satisfy $\frac{1}{2}\leq a,b,c,d\leq 2$ and $abcd=1$. Find the maximum value of $$\left(a+\frac{1}{b}\right)\left(b+\frac{1}{c}\right)\left(c+\frac{1}{d}\right)\left(d+\frac{1}{a}\right)\text{.}$$