Question

Maximize the function x + y – z = 1 with respect to the constraint xy=36.

(a) 0

(b) -8

(c) 8

(d) No Maxima exists

I have been asked this question by my college professor while I was bunking the class.

This intriguing question comes from Lagrange Method of Multiplier to Find Maxima or Minima in division Maxima and Minima of Engineering Mathematics

Answer 1

Correct choice is (d) No Maxima exists

To elaborate: Geometrically, we can see that the level curves can go further the origin along the curve xy=36 infinitely and still not reach its maximum value. What the Lagrange multiplier predicts in this case is the minimum value.