# Question:Parameterized solutions

## Question:Parameterized solutions

Maple
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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