How to Plot Surface with Coordinates?

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Pablo
Pablo on 24 Aug 2014
I am putting the question directly from the problem's perspective even though it is specifically concerned with the plotting part. I am giving the details so that I do not end up misguiding any reader.
Suppose 1 unit of power must be distributed among three users who will respectively have powers a, b and c. So obviously
a+b+c=1 and a, b, c are non-negative.
Now given the powers, the users will have utilities x, y and z. Clearly for different power allocations (with the constraints) we will have different utilities x, y and z which can be calculated from a, b, c. I want to plot the surface of (x, y, z) when the a, b, and c vary within their allowable range. I tried to figure something out with the mesh or the plot3d commands, but nothing so far. Any help please? Thanks in advance.

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