Hello everybody
Mathematica is really great! I am new here and I kindly wanted to ask you a question about solving an inequality with parameters.
So, I firstly solved the following expression (with all the parameters >0):
FullSimplify [ Reduce [ (Gu A h - A Gr - P h + r) / (2 b N + N T) > (Gu A h - A Gr - P h) / (2 b N)
&& h > 0 && b > 0 &&T > 0 && r > 0 && N > 0 && Gu > 0 && A > 0 && Gr > 0 ]]
which gave me as a result:
T > 0 && r > 0 && h > 0 && Gu > 0 && Gr > 0 && b > 0 && A > 0 && N > 0 && A Gu h T < 2 b r + A Gr T + h P T
(and this was ok)
The problem is that now, I wanted to introduce an additional parameter (D<1)
Rewriting the expression:
FullSimplify [ Reduce [ (Gu A h^D - A Gr - P h + r) / (2 b N + N T) > (Gu A h^D - A Gr - P h) / (2 b N)
&& h > 0 && b > 0 &&T > 0 && r > 0 && N > 0 && Gu > 0 && A > 0 && Gr > 0 && D<1 ]]
I get:
" Reduce::nsmet: This system cannot be solved with the methods available to Reduce. "
and I also get as Out:
Reduce[b N (2 b + T) (2 b r + (A (Gr - Gu h^D) + h P) T) > 0 &&h > 0 && b > 0 && T > 0 && r > 0 && N > 0 && Gu > 0 && A > 0 && Gr > 0 && D < 1]
So my question is: if I cannot solve the system with this new parameter D<1 (but why????) what is this result?
I apologize if this question looks stupid but it is giving me a lot of problems and I don't know how to solve it!
Thank you very much, in the case someone would like to help me!
Kodi