Question: : 3. (30 marks) Consider the following three maximization problems max f (x,y) I s.t. g2 (x, y) 3. (30 marks) Consider the following three

3. (30 marks) Consider the following three maximization problems 11 111 max

: 3. (30 marks) Consider the following three maximization problems max f (x,y) I s.t. g2 (x, y)

3. (30 marks) Consider the following three maximization problems 11 111 max f (x, y) 91 (X, y) Cl s.t. 92 (x, y) s c2 max f (x, y) 91 (X, y) Cl s.t. 92 (x, y) < c2 max f (x, y) 91 (X, y) < s.t. 92 (x, y) < c2 Suppose the Lagrange method can be used to solve them. (a) (10 marks) For which one(s) of the three maximization problems, is the Lagrange method the most useful? Why? (b) (10 marks) For which one(s) of the three maximization problems, is the Lagrange method the least useful (useless)? Why? (c) (10 marks) For which one(s) of the three maximization problems, is the Lagrange method useful (Something between parts a and b)? Why?

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