Problem with Maximize and conditions.

*To*: mathgroup at smc.vnet.net*Subject*: [mg51046] Problem with Maximize and conditions.*From*: ncc1701zzz at hotmail.com (Nacho)*Date*: Sat, 2 Oct 2004 03:19:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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: Problem with Maximize and conditions.***From:*"Fred Simons" <f.h.simons@tue.nl>

**Re: Problem with Maximize and conditions.***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>