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China Mathematical Olympiad 2018 Q6

Source: China Hangzhou ，Dec 16 ， 2017

November 16, 2017
inequalitiesalgebraChinacombinatoricsCMO

Problem Statement

China Mathematical Olympiad 2018 Q6 Given the positive integer n,kn ,k (n>k)(n>k) and a1,a2,⋯ ,an∈(k−1,k) a_1,a_2,\cdots ,a_n\in (k-1,k) ,if positive number x1,x2,⋯ ,xnx_1,x_2,\cdots ,x_n satisfying:For any set I⊆{1,2,⋯ ,n}\mathbb{I} \subseteq \{1,2,\cdots,n\} ,∣I∣=k|\mathbb{I} |=k,have ∑i∈Ixi≤∑i∈Iai\sum_{i\in \mathbb{I} }x_i\le \sum_{i\in \mathbb{I} }a_i , find the maximum value of x1x2⋯xn.x_1x_2\cdots x_n.
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