Optimization-Arithmetic-Geometric Mean Inequality

1. Feb 16, 2009

kfoisfn

1. The problem statement, all variables and given/known data
Use the Arithmetic-Geometric Mean Inequality to minimize 3x+4y+12z to xyz=1 and x,y,z>0.

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 17, 2009

HallsofIvy

What is the "Arithmetic-Geometric Mean Inequality"?

And does "minimize 3x+4y+12z to xyz=1" mean to minimize 3x+ 4y+ 12z with the condition that xyz= 1?