So I have the following:

And I want to create an animation similar to something like:

Not necesarily 3D. Just the interative slider part. 

I want to create a slider that adjusts the value of the exponent  (from the red curve) from 1 to say, 1000. 

I also want it to show the corresponding value of   on the application.

I'm sure its pretty simple, it's just that I have no idea where to start.

I am trying to solve a constrained maximization problem. 

The starting function is the one at the top in bold. Whenever I use (1/2) or (1) as an exponent for either of the variables I get unwanted results. For x₂ (below) I am getting that result. I should be getting x₂= (3m)/(5P₂)

However, whenever I input an exponent that does not equal (1/2), I get the results I want.

What am I doing wrong?