Use Lagrange multipliers to minimize the function $f(x,y,z)=x^2+y^2+z^2$ subject to the following constraint. $x+y+z-24=0$ Assume that $x,y,$ and $z$ are positive. Calculate the minimum value of $f(x,y,z).$

$729$

$192$

$54$

$27$

$81$