Re: how to solve for all integer solutions, linear

• To: mathgroup at smc.vnet.net
• Subject: [mg109518] Re: how to solve for all integer solutions, linear
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 3 May 2010 06:11:20 -0400 (EDT)

```vars = {a, b, c, d, e, f};

eqns = Flatten[{
5 a + 3 b + 2 c + 6 d + 5 e + f == 25,
a + b + c <= 4,
d + e + f <= 5,

soln = {Reduce[eqns, vars, Integers] // ToRules};

Length[soln]

80

There are 80 solutions. Looking at only solutions for which all variables are non-zero:

Select[soln, FreeQ[#, 0] &]

{{a->1,b->1,c->2,d->1,e->1,f->2},{a->1,b->2,c->1,d->1,e->1,f->1}}

Bob Hanlon

---- me13013 <me13013 at gmail.com> wrote:

=============
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

```

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