Problem

Source: Chengdu Nov 14, 2018

Tags: inequalities, China, High School Olympiads, BPSQ, Hi



Let $a,b,c,d,e\geq -1$ and $a+b+c+d+e=5.$ Find the maximum and minimum value of $S=(a+b)(b+c)(c+d)(d+e)(e+a).$