Assignment:
Consider the functions f (x,y) = 3x2 - 4xy + y2 and g(x , y) = 5x2 - 4xy + y2 consider the problem of optimizing f(x,y) subject to the constraint g(x,y) = 4.
(a) Explain why a global minimum and a global maximum must exist.
(b) Find the global minima and global maxima
Provide complete and step by step solution for the question and show calculations and use formulas.