Re: Problem with Maximize and conditions.

*To*: mathgroup at smc.vnet.net*Subject*: [mg51069] Re: [mg51048] Problem with Maximize and conditions.*From*: DrBob <drbob at bigfoot.com>*Date*: Sun, 3 Oct 2004 05:47:46 -0400 (EDT)*References*: <200410020719.DAA26394@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

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! > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

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