Re: Optimal number of sheets
- To: mathgroup at smc.vnet.net
- Subject: [mg58368] Re: Optimal number of sheets
- From: Peter Pein <petsie at dordos.net>
- Date: Tue, 28 Jun 2005 21:57:01 -0400 (EDT)
- References: <d9r4sh$55f$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Erb, John schrieb: > Hello, > > On a given occasion, I wish to create different thicknesses of a > material, ranging > say, for example, from 1 cm to 25 cm, in increments of 1 cm. > > How can I, using Mathematica, determine the minimum number > of sheets of material I need? > The material comes in thicknesses of 1, 2, 3, 4, & 7 cm. > > Thank you, > John C. Erb > email: John_C_Erb at prodigy.net > > In[1]:= Off[General::spell1]; thickness = {1, 2, 3, 4, 7}; count = x /@ Range[Length[thickness]]; In[4]:= MatrixForm[sol = count /. Last /@ Minimize[{Total[count], count . thickness == #1 && And @@ (#1 >= 0 & ) /@ count && Element[count, Integers]}, count] & /@ Range[25]] Out[4]//MatrixForm= MatrixForm[ {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 1, 0}, {0, 1, 0, 1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 2, 0}, {0, 1, 0, 0, 1}, {0, 0, 1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 3, 0}, {0, 1, 0, 1, 1}, {0, 0, 0, 0, 2}, {0, 0, 0, 2, 1}, {0, 1, 0, 0, 2}, {0, 0, 1, 0, 2}, {0, 0, 0, 1, 2}, {0, 0, 0, 3, 1}, {0, 1, 0, 1, 2}, {0, 0, 0, 0, 3}, {0, 0, 0, 2, 2}, {0, 1, 0, 0, 3}, {0, 0, 1, 0, 3}, {0, 0, 0, 1, 3}}] -- Peter Pein Berlin