Answer
See the explanation below.
Work Step by Step
The Lagrange Multipliers Method is used to determine the maximum and minimum values of the function $f(x,y,z)$ .
$\nabla f(x,y,z)=\lambda \nabla g(x,y,z)$
This is for one constraint (let us say $g(x,y,z)$). Here $g(x,y,z)=k$
For the another constraint, let us say $h(x,y,z)$, we have:
$\nabla f(x,y,z)=\lambda_1 \nabla g(x,y,z)+\lambda_2 \nabla h(x,y,z)$. Here $h(x,y,z)=c$
