Transcript of page 1 of the Hotel Østerport note.

Dear Bob, 

While drinking beer yesterday several ideas came about our maximization problem and the question of root selection. You have probably solved the problem by now, but here are a few points anyhow. First, as you know, the solution is a simple saddle point of [equation], gotten by setting both partials to zero. The problem is how to select between the 3 roots which sometimes occur. I have thought a little about why the “magic” multipliers (Lagrange) work to express constraints, and will try to briefly give you the picture: If we have a function f(xi) to be maximized subject to constraints gj(xi) = cj,[?] then we can picture the constraints as limiting our region of interest to a “surface” (subspace) within the xi space. [erasure] There is in fact a whole family of surfaces which can be labeled by the value of the gj(xi) which are constant over any one surface. 

If we now choose some fixed values [lambda]1, [lambda]2     [lambda]n

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