$\text { Find three positive numbers whose sum is } 291 \text { and whose product is a maximum. }$
A) $x = y = z = 97$
B) $x = 109 , y = 99 , z = 89$
C) $x = 100 , y = 108 , z = 89$
D) $x = 99 , y = z = - 99$
E) $x = 129 , y = 79 , z = 89$

Question

$\text { Find three positive numbers whose sum is } 291 \text { and whose product is a maximum. }$ 
A) $x = y = z = 97$
B) $x = 109 , y = 99 , z = 89$
C) $x = 100 , y = 108 , z = 89$
D) $x = 99 , y = z = - 99$
E) $x = 129 , y = 79 , z = 89$

Quizplus · Accepted Answer

The maximum product of numbers with a fixed sum is achieved when the numbers are as close to each other as possible, due to the arithmetic mean-geometric mean inequality. In this case, dividing 291 by 3 gives 97, so the numbers are 97, 97, 97.

Find three positive numbers whose sum is 291 and whose product is a maximum. \text { Find three positive numbers whose sum is } 291 \text { and whose product is a maximum. } Find three positive numbers whose sum is 291 and whose product is a maximum.

$\text { Find three positive numbers whose sum is } 291 \text { and whose product is a maximum. }$