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    Lagrangian multipliers and drawing schemes

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    1) Who can explain me Lagrangian multipliers with drawings scheme etc...
    1)I just can't imagine what is happening in space with Lagrangian multipliers.

    2) I did this problem but here also I can't understand it, because I can't understand what is happening in space! could you explain it with drawings and schemes please : the atmospheric pressure in a region near the origin is given by the formula P=30+(x+1)(y+2)exp(z).
    Approximately where is the point closest to the origin at which the pressure is 31.1 ?

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    Solution Preview

    1) Lagrangian multipliers are used in Lagrangian method, which is to minimize a function subject to some constraints.
    If the problem is
    min f(x)
    subject to h(x)=0
    then we set L(x,lamda)=f(x)-lamda*h(x) and want to find the minimum of L(x,lamda, where lamda is the Lagrangian multiplier. If we have k constraints, then we should have k Lagrangian multipliers.

    We use Lagrangian method to transform a constraint-problem into unconstraint-problem.

    I'm not sure about your first question, but I ...

    Solution Summary

    This explains and shows how to use Lagrangian multipliers.