Re: Problem with Maximize and conditions.
- To: mathgroup at smc.vnet.net
- Subject: [mg51068] Re: Problem with Maximize and conditions.
- From: "Curt Fischer" <crf3 at po.cwru.edu>
- Date: Sun, 3 Oct 2004 05:47:45 -0400 (EDT)
- References: <cjlna7$q7f$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Nacho wrote: [...] > > 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 [...] If you multiply the constraint equation by 20, NMinimize [] , but not Minimize, will get you to the correct answer. I'll leave it for the more qualified to ponder about why. In[1]:= Minimize[{x+y+z,xâ??Integers,yâ??Integers,zâ??Integers,1â?¤x,98â?¥x,1â?¤y,98â?¥y,1â?¤z,98â?¥z, x+20y+100z\[Equal]2000},{x,y,z}] Out[1]= Minimize[{x+y+z,xâ??Integers,yâ??Integers,zâ??Integers,1â?¤x,98â?¥x,1â?¤y,98â?¥y,1â?¤z,98â?¥z, x+20 y+100 z\[Equal]2000},{x,y,z}] In[2]:= NMinimize[{x+y+z,xâ??Integers,yâ??Integers,zâ??Integers,1â?¤x,98â?¥x,1â?¤y,98â?¥y,1â?¤z,98â?¥z , x+20y+100z\[Equal]2000},{x,y,z}] Out[2]= {43.,{x\[Rule]20,y\[Rule]4,z\[Rule]19}} -- Curt Fischer