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Question

 Consider the following optimization problem: 


Max x12+

x22 

subject to : 5x12+ 6x1x2 + 5x22 ≤ 1 


where x1 and x2 are choice variables:


1) Write the Lagrangean and the Kuhn-Tucker conditions.

2)State and verify the second order condition. Distinguish between sufficient and necessary condi-

tions.

3)Is the constraint qualification condition satisfied? Show clearly why or why not.

4) Solve the Kuhn-Tucker conditions for the optimal choice: x1, x2 and λ, Use the second order

condition to analyze your solution and determine which of your stationary points is a maximum. 

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