hw2 - (a) max & 1 x + 1 y s.t. & 1...

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ECON 401: Assignment 2 due date: September 21, 2011 1. Find and classify the critical points (local maximum, local minimum, neither) of the each of the following functions. Are any of the local optima also global optima? (a) f ( x; y ) = x 1+ x 2 + y 2 2. Let f : R n ! R be a twice di/erentiable function. Consider g : R n ! R such that g ( x ) = f ( x ) . Prove that D 2 f ( x ) D 2 g ( x ) is negative 3. Solve the following optimization problems.
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Unformatted text preview: (a) max & 1 x + 1 y s.t. & 1 x 2 + & 1 y 2 = 1 : (b) min & 1 x + 1 y s.t. & 1 x 2 + & 1 y 2 = 1 : 4. Solve the following optimization problems. (a) max ( xyz ) s.t. ( x + y + z ) = 5 and ( xy + yz + zx ) = 8 : (b) min ( xyz ) s.t. ( x + y + z ) = 5 and ( xy + yz + zx ) = 8 : 1...
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