(Step-by-Step) Use Lagrange multipliers to find the indicated extrema Maximize f(x,y,z)=x^2+y^2+z^2 , s.t. x+2z=6 , x+y=12
Question: Use Lagrange multipliers to find the indicated extrema
\[\begin{aligned} & \text{Maximize}\,\,\,\,\,f\left( x,y,z \right)={{x}^{2}}+{{y}^{2}}+{{z}^{2}} \\ & \text{s}\text{.t}\text{.}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+2z=6 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y=12 \\ \end{aligned}\]
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