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Econ617Fall2005FinalExam15Dec2005

# Econ617Fall2005FinalExam15Dec2005 - Economics 617 Final...

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December 16, 2005 Economics 617 Final Exam 1. This exam has four questions. You have 2 hours and 30 minutes to write the exam. 2. This is a closed-book exam. 3. If you find any question ambiguous, explain your confusion and make whatever assumptions you think are necessary to answer the question. Clearly state any additional assumption you make. GOOD LUCK! 1

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1. [An Application of Weierstrass Theorem] [(a) =10 points, (b) = 20 points, (c) = 20 points] The primal ( P ) and dual ( D ) problems in linear programming are written as follows: Max q x Subject to Ax b and x 0 ( P ); Min y b Subject to y A q and y 0 ( D ) where q is 1 × n, A is m × n, x is n × 1 , b is m × 1 and y is 1 × m. Define the set of feasible solutions to the Primal as: F ( P ) = { x 0 such that Ax b } and the set of feasible solutions to the Dual as: F ( D ) = { y 0 such that y A q } Assume that there is ¯ x F ( P ) , and there is ¯ y F ( D ) . Further, assume that q R n ++ .
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