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## Homework Statement

Minimize f(X, Y, Z) = 2XY + 6YZ + 8XZ subject to the constraint XYZ = 12.

## Homework Equations

The gradients of the equations, and XYZ = 12.

## The Attempt at a Solution

I have the gradients for both of the equations.

∇f = <2Y + 8Z, 2X + 6Z, 6Y + 8X> ∇g = < YZ, XZ, XY> I also have XYZ 12.

I have set them up in there separate equations with the λ in them. I have just stuck on how to solve them. Isn't there a way to plug the equations in the my TI - 83 Plus to solve them?