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