Re: Re: Problem with Maximize and conditions.

• To: mathgroup at smc.vnet.net
• Subject: [mg51231] Re: [mg51213] Re: Problem with Maximize and conditions.
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 9 Oct 2004 04:18:54 -0400 (EDT)
• References: <cjlna7\$q7f\$1@smc.vnet.net> <cjoiig\$alt\$1@smc.vnet.net> <cjr9ea\$ost\$1@smc.vnet.net> <200410050837.EAA08385@smc.vnet.net> <ck0b8c\$nr7\$1@smc.vnet.net> <ck33j9\$av4\$1@smc.vnet.net> <200410080655.CAA25027@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Is this what you meant to enter in your e-mail?

Minimize[{x + y + z,
{(1/20)*x + y + 5*z >= 100,
(1/20)*x + y + 5*z <= 102,
x \[Element] Integers,
y \[Element] Integers,
z \[Element] Integers,
0 < x < 99, 0 < y < 99,
0 < z < 99}}, {x, y, z}]
{22, {x -> 1, y -> 1, z -> 20}}

I had to guess what "&#8805;", "&#8804;" and "&#8712" represent. For things like this, I recommend Omega Consulting's "Copy as InputForm" palette at

http://eclecticdreams.net/DrBob/copy_as_inputform.htm

or Ingolf Dahl's palette at

If I guessed the right substitutions, tightening the second inequality gives the following under version 5.0.1 (with no kernel crash):

Minimize[{x + y + z,
{(1/20)*x + y + 5*z >= 100,
(1/20)*x + y + 5*z <= 101,
x \[Element] Integers,
y \[Element] Integers,
z \[Element] Integers,
0 < x < 99, 0 < y < 99,
0 < z < 99}}, {x, y, z}]
{25, {x -> 1, y -> 5, z -> 19}}

Bobby

On Fri, 8 Oct 2004 02:55:17 -0400 (EDT), Peter Valko <p-valko at tamu.edu> wrote:

> Hi,
>
> Of course Steve was the one who solved the problem by introducing
> Reduce. Using it inside the Minimize command is a smart move, but it
> does not change the fact: the reduce function explicitely prepares the
> whole set of feasible solutions.
> As Janos Pinter and others have pointed out, complete enumeration
> works for the little example in question, but it cannot be used for
> larger problems.
>
> To get a bit nearer to the root of the problem I rewrote the original
> example as
>
> Minimize[{x + y + z, {1/20 x + y + 5z &#8805; 100, 1/20 x + y + 5z
> &#8804; 102, x
>           &#8712; Integers, y &#8712; Integers, z &#8712; Integers, 0
> < x < 99, 0 <
>         y < 99, 0 < z < 99}}, {x, y, z}]
>
> This works fine and gives the correct solution
> {22, {x -> 1, y -> 1, z -> 20}}
>
> Unfortunately, when I make the second inequality stronger, that is
> 1/20 x + y + 5z &#8804; 101
>
> then "MathKernel encounters a problem and has to close (while being
> sorry for the inconvenience.)"
>
> Appearantly, Minimize uses the Gomory-algorithm, reducing the integer
> LP into a series of classical LP problems, but somewhere on the road
> it crashes. This is a simple bug and I think the given example will
> help the developer to find it.
>
> Regards
> Peter
>
>"Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk> wrote in message news:<ck33j9\$av4\$1 at smc.vnet.net>...
>> Yes, I knew that, because my first reply listed the full output of Reduce!
>> However, I overlooked the possibility that immediately substituting this
>> output back into Minimize would work.
>>
>> Steve Luttrell
>>
>> "Andrzej Kozlowski" <akoz at mimuw.edu.pl> wrote in message
>> news:ck0b8c\$nr7\$1 at smc.vnet.net...
>> >
>> > On 5 Oct 2004, at 17:37, Steve Luttrell wrote:
>> >
>> >> It seems
>> >> that the conditions you feed to Minimize are "improved" by being
>> >> wrapped in
>> >> Reduce.
>> >>
>> >
>> > Well, they are not just "improved" but actually "Reduced" to
>> > triviality. Reduce does all the work and Minimize is only left with
>> > something that looks like this (except that with more terms)
>> >
>> >
>> > Minimize[x + y + z, {x == 20 && y == 4 && z == 19 ||
>> >     x == 20 && y == 9 && z == 18}, {x, y, z}]
>> >
>> >
>> > This sort of thing even Minimize can manage;-)
>> >
>> >
>> > Andrzej Kozlowski
>> > Chiba, Japan
>> > http://www.akikoz.net/~andrzej/
>> > http://www.mimuw.edu.pl/~akoz/
>> >
>
>
>
>

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

```

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