Re: About linear programming

*To*: mathgroup at smc.vnet.net*Subject*: [mg126241] Re: About linear programming*From*: Dana DeLouis <dana01 at me.com>*Date*: Thu, 26 Apr 2012 05:32:02 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> 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? Hi. I believe the problems are caused by being Unbounded in the Negative direction. Just add a lower limit that each variable is >= 0. obj = 5 Subscript[x,1]+4 Subscript[x,2]+3 Subscript[x,3] ; const = { Subscript[x,1]+Subscript[x,3]<=15, Subscript[x,2]+2 Subscript[x,3]<=25, Subscript[x,1]>=0, Subscript[x,2]>=0, Subscript[x,3]>=0} var = { Subscript[x,1], Subscript[x,2], Subscript[x,3]} Maximize[{obj ,const},var] {175, {Subscript[x, 1]->15, Subscript[x, 2]->25, Subscript[x, 3]->0}} When one has many variable as in your example #2, try including Thread, as in this small example... Thread[var >= 0] {Subscript[x, 1]>=0,Subscript[x, 2]>=0,Subscript[x, 3]>=0} Don't know if you would find this useful: Although LinearProgramming is a Minimizing function, one can multiply the objective by -1 to reverse the logic. This changes your Maximizing problem into one of Minimizing. obj ={5,4,3}; LinearProgramming[ - obj, {{1,0,3},{0,1,2}}, {{15,-1},{25,-1}} ] {15,25,0} obj . % 175 = = = = = = = = = = Good luck. HTH :>) Dana DeLouis Mac & Math 8 = = = = = = = = = = On Apr 25, 12:35 am, Marcela Villa Marulanda <mavim... at gmail.com> wrote: > 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]}]