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Editorial Team
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Asked: 2026-06-04T07:40:31+00:00

I need to make a linear programming model. Here are the inequalities I’m using

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I need to make a linear programming model. Here are the inequalities I’m using (for example):

6x + 4y <= 24
x + 2y <= 6
-x + y <= 1
y <= 2

I need to find the area described by these inequalities, and shade it in a graph, as well as keep track of the vertices of the bounding lines of this area, and draw the bounding line in a different color. See the graph below for an example of what I’m looking for.

image of the points of intersection.

I’m using Python 3.2, numpy, and matplotlib. Are there better modules for linear programming in Python?

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1 Answer

  1. Editorial Team

    UPDATE: The answer has become somewhat outdated in the past 4 years,
    here is an update. You have many options:

    • If you do not have to do it Python then it is a lot more easier to
      do this in a modeling langage, see Any good tools to solve
      integer programs on linux?

    • I personally use Gurobi these
      days through its Python API. It is a commercial, closed-source
      product but free for academic research.

    • With PuLP you can create MPS and LP files and then
      solve them with GLPK, COIN CLP/CBC, CPLEX, or XPRESS through their
      command-line interface. This approach has its advantages and
      disadvantages.

    • The OR-Tools from Google is an open source software suite for optimization, tuned for tackling the world’s toughest problems in vehicle routing, flows, integer and linear programming, and constraint programming.

    • Pyomo is a Python-based, open-source optimization modeling language with a diverse set of optimization capabilities.

    • SciPy offers linear programming: scipy.optimize.linprog. (I have
      never tried this one.)

    • Apparently, CVXOPT offers a Python interface to GLPK, I did
      not know that. I have been using GLPK for 8 years now and I can
      highly recommend GLPK. The examples and tutorial of CVXOPT seem really nice!

    • You can find other possibilites at in the Wikibook under
      GLPK/Python. Note that many of these are not necessarily resticted
      to GLPK.

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