Answer to Question #38331 in Calculus for yamada

Question

Minimize the function f subject to two constraints:f(x,y,z)=xyz on the intersection of x^2+y^2-1=0 and x-z=0
Here we have two constraints g1=0 and g2=0 and thus need two multipliers λ and μ and the system becomes ∇f =λ∇g1+μ∇g2, g1=0 , g2=0.