```Date: Apr 30, 2013 1:57 PM
Author: gus gassmann
Subject: Re: Is it possible to maximize/minimize several variables in LP?

On 30/04/2013 1:25 PM, Xu Wang wrote:> Hello,>> I want to maximize (or minimize) several variables in a LP problem as following.>> maximize: x1 + x2 + x3> subject to: constrains contain xi, i = 1, ..., n>> When the object function is maximized, are the values of x1, x2 and x3 maxmized?Depends on what you mean by "maxmized". Let's look at a simple example:max x1 + x2 + x3s.t. x1 + 2 x2 + 3 x3 <= 10      x1 >= 0,      x2 >= 0,      x3 >= 0Any linear programming solver (and there are many, including several open-source solvers) will report as optimal solution x1 = 10, x2 = 0, x3 = 0. However, this clearly does not "maximize" x2, as x1=0, x2=5, x3=0 satisfies the constraints, and so x2 _could_ be as high as 5.When you have multiple objectives (i.e., you truly want to maximize --- in some sense --- x1 AND x2 AND x3), an ordinary linear programming solver is not going to help you much. Look up "Multi-objective programming" or "Pareto optimum" on the internet. That should get you started, at least.> Thank you in advance.>> Regards,> Xu>
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