Parameterized solutions
Hi,
I'm new at Maple, trying to migrate from Mathcad but I'm getting stuck on a basic problem.
I want Maple to find numeric solutions to a maximization problem and express the solution as a function of the problem's parameters.
To take a very simple example of the more general thing I want to do, suppose I have a profit function which is a function of inputs T and L and factor prices w and r.
F:=(T,L)->T^(1/2)*L^(4/5);
Profit := (T, L, w, r) -> F(T, L)-w*L-r*T;
I seem to be able to almost isolate the parameterized functions I want as follows:
T := (w, r) -> Maximize(Profit(T, L, w, r), assume = nonnegative)[2][1];
L := (w, r) -> Maximize(Profit(T, L, w, r), assume = nonnegative)[2][2];
But it seems this is not quite the form I need to start using these values (for plots, substitutions, etc). For instance the solutions at w=r=0.5 are:
>T(.5, .5);
T = 0.409599999856571140
> L(.5, .5);
L = 0.327679999848665248
But when I plug these back into say F(T,L) I get:
> F(T(.5, .5), L(.5, .5));
Error, (in F) non-algebraic base in a power
I'm obviously missing something basic. Any suggestions? Any more elegant way to approach my overall problem?
Thanks!
Jonathan
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