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Math Help - Lagrange Multplier

  1. #1
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    Lagrange Multplier

    I have to maximise  2 \tan ^{-1} (x_{1}) + x_{2} subject to  x_{1} + x_{2} \le b_{1} and  - \log (x_{2}) \le b_{2} for constants  b_{i} satisfying  b_{1} - e^{-b_{2}} \ge 0 where  x_{i} \ge 0 .

    Clearly it is easy to write down the Lagrangian and get that  L_{x_{1}} = \frac{2}{1 + x_{1} ^{2} } - \lambda = 0 and  L_{x_{2}} = 1 - \lambda + \frac{ \mu }{x_{2}} = 0 .

    Note that slacked variables have been used to take care of the inequality constraints. I don't know how to proceed. Clearly I could solve the equations I have from differentiation however taking into account that I have inequalities for constraints I am rather confused. What can I do here?
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  2. #2
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    Anyone?
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  3. #3
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    I hate to bump this twice but I am still stuck. Does anyone have any ideas, even if you can't get the full answer?
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