Question

If \(A, B, C,\) and \(D\) are positive numbers such that \(A + 2B + 3C + 4D = 8\), then what is the maximum value of \(ABCD\)?

Any help is appreciated, these are precalc problems. Thanks!

Answer 1

you may use AM-GM inequality :

\[(A*2B*3C*4D)^{1/4} \le \dfrac{A+2B+3C+4D}{4}\]

Answer 2

where is that formula from ?

Answer 3

https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means#The_inequality

Answer 4

thanks!