Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.
$$f ( x , y , z , t ) = 7 x + 7 y + 7 z + 7 t , \quad 7 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + t ^ { 2 } \right) = 8$$

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The Answer of Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.
$$f ( x , y , z , t ) = 7 x + 7 y + 7 z + 7 t , \quad 7 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + t ^ { 2 } \right) = 8$$

Use Lagrange Multipliers to Find the Minimum Value of the Function