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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)