Re: Problem with Maximize and conditions.

*To*: mathgroup at smc.vnet.net*Subject*: [mg51101] Re: Problem with Maximize and conditions.*From*: ncc1701zzz at hotmail.com (Nacho)*Date*: Mon, 4 Oct 2004 06:18:33 -0400 (EDT)*References*: <200410020719.DAA26394@smc.vnet.net> <cjoj5g$ap6$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hello Dr.Bob. I don't understand very well all thoise # and @ yet ;) I'm on it... But it seems you're using brute force. It is nice to see how to use brute force when all the other methods works. Thanks for your solution. Best regards. DrBob <drbob at bigfoot.com> wrote in message news:<cjoj5g$ap6$1 at smc.vnet.net>... > Minimize and NMinimize apparently can't solve this simple Integer problem; I'm sure somebody will explain to you why this is a good thing, but I can't. > > Meanwhile, here's an answer the hard way: > > Timing[feasible = Select[Flatten[ > Outer[List, Range@98, Range@98, Range@98], 2], {1/20, 1, 5}.# == 100 &]; > {Tr@#, #} &@First@feasible[[Ordering[feasible, -1, Tr@#1 > Tr@#2 &]]]] > > {9.687 Second,{43,{20,4,19}}} > > and here's a much faster solution: > > Timing[feasible = Select[ > Flatten[Outer[List, Range[98], > Range[98]], 1] /. > {x_, z_} -> {x, 100 - x/20 - > 5*z, z}, > 1 <= #1[[2]] <= 98 && > #1[[2]] \[Element] Integers & ]; > ({Tr[#1], #1} & )[ > First[feasible[[Ordering[ > feasible, -1, > Tr[#1] > Tr[#2] & ]]]]]] > > {0.078 Second, {43, {20, 4, 19}}} > > Bobby > > On Sat, 2 Oct 2004 03:19:15 -0400 (EDT), Nacho <ncc1701zzz at hotmail.com> wrote: > > > Hello. > > > > I was trying to solve a problem with Mathematica 5 and I am getting > > strange results. > > > > The problem is: > > > > Minimize x+y+z, with the condition that 1/20x+y+5z==100 and x,y,z are > > Integers between 1 and 98 (inclusive). > > > > So I use: > > > > Minimize[{x+y+z, 1/20 x+y+5z\[Equal]100, x \[Element] Integers, > > y \[Element] Integers, z\[Element]Integers, 0<x<99,0<y<99,0<z<99}, > > {x,y, > > z}] > > > > I have copied the text using "Plain text" option, I hope it's fine. > > > > This returns the same expression, I suppose that Mathematica cannot > > resolve it. So I use NMinimize: > > > > NMinimize[{x+y+z, 1/20 x+y+5z\[Equal]100, x \[Element] Integers, > > y \[Element] Integers, z\[Element]Integers, 0<x<99,0<y<99,0<z<99}, > > {x,y, > > z}] > > > > Now I get a result, but rather weird... > > > > \!\({25.`, {x -> 1, y -> 5, z -> 1899\/100}}\) > > > > The minimum of x+y+z is 25 but z is 1899/100 > > 1899/100 is not a Integers, and the nearest Integer, 19, doesn't > > satisfy 1/20x+y+5z==100, and also x+y+z is not 25 but 24.99 > > > > I don't know why Mathematica has returned a Real when I specified an > > Integers. I suppose that it is related to the use of NMinimize. I > > suppose that it considers that 18.99 is so near of 19 that it can be > > considered an Integer. > > > > If you remove the condition of z being an Integer, the result changes, > > so it is affecting. Also, if you ask for "1899/100 e Integers" it > > returns False. > > > > So, does anybody know how to solve this? Ideally, I would like to know > > why Minimize doesn't work (so I have to use NMinimize), but in any > > case, how to solve the problem. > > > > Thanks! > > > > > > > >

**Follow-Ups**:**Re: Re: Problem with Maximize and conditions.***From:*DrBob <drbob@bigfoot.com>

**References**:**Problem with Maximize and conditions.***From:*ncc1701zzz@hotmail.com (Nacho)