Consider the following NLP

Minf$(x,y,z)=x^2+(y-2{)}^2+(z-1{)}^2$

s$.$t$.g(x,y,z)=4x+y+4z-39$

To solve the above NLP we first construct the Lagrangian function:

$L(x,y,z,)=f(x,y,z)-g(x,y,z).$

Which gives that:

The solution is $x=6\mathrm{.}36,y=3715,z=7\mathrm{.}86,$ and

$=343$

The value of $f$ is $9706$