Problem
ALG-B2-M04-P002 Extreme elements
#2
★★☆☆☆ Level 2 of 5
Let \(a\le b\le c\) and \(x\le y\le z\). Prove that \(az+by+cx\le ax+by+cz\).
Hint. The middle term is the same. Compare only the pairs \(a,c\) and \(x,z\).
The difference between the right and left sides is \(ax+cz-az-cx=(c-a)(z-x)\ge0\). Hence the inequality holds.
A useful understanding check: the student should see that the problem reduces to the two extreme elements.