Find the maximum value of 2x + 2y + z on the sphere of radius 1 at the origin.
Since the value of is not part of the solution, you can often simplify by first eliminating by dividing one equation by another.
Here, you have and so, dividing the first by the second,
so that
or y= x. Similarly, dividing by gives x= 2z.
Putting those into gives .