Minimize
subject to
. The Lagrangian would be
and has partial derivatives
Setting each partial derivative to 0, we have
From the third equation, it follows that either
or
. In the second case, we arrive at a contradiction:
since both
and
must be non-negative, yet this would mean e.g.
. So it must be that
.
The first and second equations then tell us that
from which we obtain
.
Thus the points on the cone closest to (16, 6, 0) are
.