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.

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!
> >
> >
> >
> >

```

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