Question

Minimize the function f subject to two constraints:
f(x,y,z)=xyzon 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