Use Lagrange Multipliers to Find the Maximum and Minimum Values $f ( x , y , z ) = 5 x - y - 5 z \quad$

Short Answer

Use Lagrange multipliers to find the maximum and minimum values of the function $f ( x , y , z ) = 5 x - y - 5 z \quad$ subject to the constraints $x + 2 y - z = 0$ and $x ^ { 2 } + 4 y ^ { 2 } = 1$ .