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Find max and/or min P

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September 15, 2010
InequalitymaximizationcalculusoptimizationlagrangeIMO ShortlistIMO Longlist

Problem Statement

Given real numbers x1,x2,…,xn (n≥2)x_1, x_2, \dots , x_n \ (n \geq 2), with xi≥1n (i=1,2,…,n)x_i \geq \frac 1n \ (i = 1, 2, \dots, n) and with x12+x22+⋯+xn2=1x_1^2+x_2^2+\cdots+x_n^2 = 1 , find whether the product P=x1x2x3⋯xnP = x_1x_2x_3 \cdots x_n has a greatest and/or least value and if so, give these values.
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