My Math Forum Optimization Problem with Constraint

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 December 8th, 2009, 02:40 AM #1 Newbie   Joined: Dec 2009 Posts: 1 Thanks: 0 Optimization Problem with Constraint I have a (maybe trivial?) question on constrained optimization. Assume that I have the following maximization problem: \max_{x,y} -2x^{2}+3xy-3y^{2} -10x-10y, subject to -2x^{2}+3xy-10x >= 0. I setup the Lagrangian and I get the following first order conditions with the lagrange multiplier \lambda. -4x + 3y - 10 + \lambda (-4x + 3y -10) = 0, 3x -6y - 10 + \lambda (3x) = 0. By the Kuhn Tucker conditions, we know that if \lambda > 0, then the constraint is binding. However, from the first order conditions, we can see that the multiplier \lambda is negative! How can this be? Am I doing things wrong here? I know that this could mean that the constraint is always non-binding. But what if we changed the constraint to -2x^{2}+3xy-10x \geq 100. This clearly has an effect on the problem. So does this mean that the regularity condition (constraint qualification) is violated? Please help! Thank you

### what is first order condition in economics

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