Use Lagrange multipliers to find the indicated extrema of subject to two constraints. In each case,
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Use Lagrange multipliers to find the indicated extrema of ƒ subject to two constraints. In each case, assume that x, y, and z are nonnegative.
Minimize ƒ(x, y, z) = x² + y² + z²
Constraints: x + 2z = 6, x + y = 12
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