If w, x, y, and z are positive real numbers such that w + 2x + 3y + 4z = 8 then what is the maximum value of wxyz?

Guest Oct 11, 2021

#3**+2 **

The correct answer is 2/3 because you get (w+2x+3y+4z)/4 >= 4rt(24wxyz) which becomes 8/4 >= 4rt(24wxyz) so you get 2^4 >= 24wxyz. This simplifies to 16/24=2/3=wxyz.

Tacoeggegg Oct 12, 2021

edited by
Guest
Oct 12, 2021

#6**+1 **

You use the AM-GM inequality which says (a_1+a_2+a_3+...+a_n)/n >= nrt(a_1*a_2*...*a_n). Here's the art of problem solving article https://artofproblemsolving.com/wiki/index.php/Arithmetic_Mean-Geometric_Mean_Inequality

Tacoeggegg
Oct 12, 2021

#9**0 **

I agree my answer is not correct but there is not enough information on that linked page for your answer to be reached.

You should not be dividing by 4 you should be dividing by 10. (to get the arithemtic mean)

the numbers are w,x,x,y,y,y,z,z,z,z, There are 10 numbers.

Perhaps you would like to provide more working or another link address that you used.

Melody
Oct 14, 2021