CODEWITHSUNDEEP
wolfram-mathematicamaximize
benalbert342
benalbert342

Reputation: 71

Mathematica Does No Find the Global Maximum It Just Print Out My Function

I am am mathmatica notebook to find an analytical solution to the follow constrained optimization problem: Max y^(1-b)(x^b(1-a(x/(x+1)))) s.t. M = Px+qy x,y I have tried the following code:

Maximize[{y^(1-b)(x^b(1-a(x/(x+1)))), M==Px+qy}, {x,y}]

and in returns the same function as an output. In the function a, b, M, P, and q are all parameters. I have also tried assigning the parameters arbitrary values to test to see if mathmatica is not sure how to deal with the parameters. I used to following code:

Maximize[{y^(1-0.5)(x^0.5(1-0.75(x/(x+1)))), 1000=5x+5y},{x,y}]

and it returns the same function. However, if I remove the constraint it will solve the optimization problem. 

Maximize[{y^(1-0.5)(x^0.5(1-0.75(x/(x+1))))},{x,y}]
{7.2912*^59,{x->2.89727*^60,y->2.93582*^60}}

I am not sure what to do. After reading about constrained optimization problem the syntax appears to be correct. Sorry, it this question is really basic I am very new to mathmatica, also since I am using a notebook I could not past the output from the first two lines in.

Upvotes: 0

Views: 544

Answers (1)

Rohit Namjoshi
Rohit Namjoshi

Reputation: 679

The constraint is incorrectly specified, it should be 1000 == 5 x + 5 y. Maximize works better with exact numbers.

Maximize[{Rationalize[y^(1 - 0.5) (x^0.5 (1 - 0.75 (x/(x + 1))))], 
   1000 == 5 x + 5 y}, {x, y}] // N

(* {25.7537, {x -> 96.97, y -> 103.03}} *)

Upvotes: 1

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