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how to solve for all integer solutions, linear programming

• To: mathgroup at smc.vnet.net
• Subject: [mg109505] how to solve for all integer solutions, linear programming
• From: me13013 <me13013 at gmail.com>
• Date: Sun, 2 May 2010 05:35:33 -0400 (EDT)

Howdy,

I have a small linear programming problem that I would like to solve
for all integer solutions:

  5a + 3b + 2c + 6d + 5e + f = 25
  a + b + c <= 4
  d + e + f <= 5
  a,b,c,d,e,f >= 0

How can I pose this problem to Mathematica?

I have looked at (and fiddled around with) the LinearProgramming
function, but I don't see how to make ti give me the solution(s) I am
looking for.

Thanks for any help,
Bob H