Optimization-Arithmetic-Geometric Mean Inequality

[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

[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?