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