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Given a function $g(x,y,z)$ we need to maximize it given constraints $a.

If the constraints were given as a function $f(x,y,z)$ the following equation could be used.

$\nabla f(x,y,z) = \lambda \nabla g(x,y,z)$

How would I set up the initial equation given an interval constraint. Or how would I turn the interval constraint into a function constraint.

EDIT:: Added $a to the constraints.

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    Hint: consider a function such as $(x-(a+b)/2)^2$2012-11-10

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Maximize $g$ ignoring the constraint. If the solution fulfills the constraint, you're done. If not, there's no maximum, since it would have to lie on the boundary, but the boundary is excluded by the constraint.

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    @Kassym: Your question has little to do with the problem in that image, which does indeed require Lagrange multipliers. Next time please take more care in describing the problem, or provide$a$verbatim quote or link right away; that would have saved everyone$a$lot of time.2012-11-11