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About linear programming

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126207] About linear programming
  • From: Marcela Villa Marulanda <mavima10 at gmail.com>
  • Date: Wed, 25 Apr 2012 00:33:49 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi,

I attempt to solve these linear programming problems in Mathematica,
but its result is "Maximize::natt: The maximum is not attained at any
point satisfying the given constraints", why? I've solved this problem
in other applications and the solution is achieved.

I don't know the reasons about it. I'll thank to whom give me some
clues!

Problem 1

Maximize[{5 Subscript[x, 1] + 4 Subscript[x, 2] + 3 Subscript[x, 3],
   Subscript[x, 1] + Subscript[x, 3] <= 15 &&
    Subscript[x, 2] + 2 Subscript[x, 3] <= 25}, {Subscript[x, 1],
   Subscript[x, 2], Subscript[x, 3]}];

Problem 2

Maximize[{30 Subscript[x, 1] + 40 Subscript[x, 2] +
   20 Subscript[x, 3] + 10 Subscript[x, 4] - 15 Subscript[x, 5] -
   20 Subscript[x, 6] - 10 Subscript[x, 7] - 8 Subscript[x, 8],
  0.3 Subscript[x, 1] + 0.3 Subscript[x, 2] + 0.25 Subscript[x, 3] +
     0.15 Subscript[x, 4] <= 1000 &&
   0.25 Subscript[x, 1] + 0.35 Subscript[x, 2] +
     0.3 Subscript[x, 3] + 0.1 Subscript[x, 4] <= 1000 &&
   0.45 Subscript[x, 1] + 0.5 Subscript[x, 2] + 0.4 Subscript[x, 3] +
     0.22 Subscript[x, 4] <= 1000 &&
   0.15 Subscript[x, 1] + 0.15 Subscript[x, 2] +
     0.1 Subscript[x, 3] + 0.05 Subscript[x, 4] <= 1000 &&
   Subscript[x, 1] + Subscript[x, 5] == 800 &&
   Subscript[x, 2] + Subscript[x, 6] == 750 &&
   Subscript[x, 3] + Subscript[x, 7] == 600 &&
   Subscript[x, 4] + Subscript[x, 8] == 500}, {Subscript[x, 1],
  Subscript[x, 2], Subscript[x, 3], Subscript[x, 4], Subscript[x, 5],
  Subscript[x, 6], Subscript[x, 7], Subscript[x, 8]}]



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