Question: Maximization of a function over a given range

I am having difficulty getting Maple to find the optimal solution over a specified range. That is, I want to limit the possible range of my maximizers. For my problem I am maximizing the expression "payoff" with respect to p and s and want to tell Maple to search for all solutions where s<pa.

I have the following expression for variable x


where x is an input to the function payoff that I wish to maximize:

payoff:=p*x + s*subs(Q=x,y) + m*(1-subs(Q=x,y)));



Now, defining the FOC of payoff as


and then using


Maple does not find a viable solution since it finds an s>pa. (The function x has an asymptote at s=pa and the optimal s must be s<pa for my problem.)

How do I find the solution (p,s) over the restricted range s<pa?

Please Wait...