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Re: question about maximization with mathematica tool

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109414] Re: question about maximization with mathematica tool
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Mon, 26 Apr 2010 04:50:39 -0400 (EDT)

Consider it in another form:

f[la_, t_, y_, x_] =
  Rationalize@
   Collect[12 la*
      t + (0.12 x +
        5 y)*((2 (42 x + 4018 y - 7 x y))/(9 x y) - (6 x + 574 y -
            x y)^2/(2025 x^2 y^2)), x]

2597248/16875 + 12 la t +
  x (-(3151/16875) - 4/(1875 y^2) + 6304/(5625 y)) - 932/(1875 y) - (
  3151 y)/405 - (329476 y)/(
  405 x^2) + (-(205492/5625) + (1809248 y)/405)/x

The first term is a constant; no problem.

The second term (12 la t) is a constant with respect to x; no problem.

The third term is x times a factor that doesn't depend on x; its maximum  
is either Infinity, -Infinity, or 0, depending on whether the factor is  
positive, negative, or zero.

The fourth and fifth terms are constant in x.

The sixth term has a maximum of Infinity (x -> 0) if y is negative, 0 (as  
x-> Infinity) if y is positive, or zero if y is zero.

The seventh term has a maximum of Infinity (as x -> 0) if the numerator is  
positive, 0 (as x -> Infinity) if the numerator is negative, or zero if  
the numerator is zero.

So... what answer would you like Mathematica to give?

Just for fun, consider the conditions for f to be larger than 10^10:

Reduce[f[la, t, y, x] > 10^10, {la, t, y, x}, Reals];
LeafCount@%

89292

Good luck with that!

Bobby

On Sun, 25 Apr 2010 05:24:34 -0500, MANOLIS <voskakis86 at gmail.com> wrote:

> i want to maximize the equation below:
>
> 12La*T + (0.12x + 5 y)*((2 (42 x + 4018 y - 7 x y))/(
>     9 x y) - (6 x + 574 y - x y)^2/(2025 x^2 y^2))
>
> it has 4 variables x, y, La, T. I want the maximization for the x
> variable only. In other words i want to find a relation between x and
> the other variables that maximizes the whole equation. the
> restrictions are that 80<x<250 and y==3.5 || y==2
>
> i wrote the command below  in mathematica but nothing:
>
>
> Maximize[{12La*T + (0.12x + 5y)*((2 (42 x + 4018 y - 7 x y))/(
>       9xy) - (6x + 574y - x*y)^2/(2025 x^2 y^2)),
>   x < 250 && x > 80, y == 3.5 || y == 2}, {x}]
>
>
> i dont know why. i dont think that it is the number of variables that
> causes the problem...
>
> thank you very much
> Manolis
>


-- 
DrMajorBob at yahoo.com


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