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Lagrangian multipliers and drawing schemes

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 ?

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.