# Solve Linear Programming Problems You then pass those matrices as arguments to the LPSOLVE subroutine.The subroutine returns the solution (and other information) in output arguments.SAS 9.3 customers can call the LP subroutine, which works similarly.

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In practice, it is often convenient to be able to specify the problem in a non-standardized form in which some of the constraints represent "greater than," others represent "less than," and others represent equality.

Computer software can translate the problem into a standardized form and solve it.

In addition to companies that license SAS/IML software, SAS/IML is part of the free SAS University Edition, which has been downloaded almost one million times by students, teachers, researchers, and self-learners.

Whereas the syntax in PROC OPTMODEL closely reflects the mathematical formulation, the SAS/IML language uses matrices and vectors to specify the problem.

The green star indicates the optimal solution, which is x = .

The theory of linear programming says that an optimal solution will always be found at a vertex of the feasible region, which in 2-D is a polygon.The following list summarizes the information that you must provide: The following SAS/IML program defines and solves the same LP problem as in the previous section.I've added plenty of comments so you can see how the elements in this program compare to the more compact representation in PROC OPTMODEL: Although the LPSOLVE function was not as simple to use as PROC OPTMODEL, it obtains the same solution. This article shows two ways to solve linear programming problems in SAS: You can use the OPTMODEL procedure in SAS/OR software or use the LPSOLVE function in SAS/IML software.A linear programming problem can always be written in a standard vector form.The LPSOLVE subroutine supports many features that are not mentioned here. The LPSOLVE subroutine was introduced in SAS/IML 13.1, which was shipped with SAS 9.4m1.The LPSOLVE function replaces the older LP subroutine, which is deprecated.His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis.Graphical Method: Owing to the importance of linear programming models in various industries, many types of algorithms have been developed over the years to solve them.For an introduction to using the OPTMODEL procedure to solve linear programming problems, see the 2011 paper by Rob Pratt and Ed Hughes.Not every SAS customer has a license for SAS/OR software, but hundreds of thousands of people have access to the SAS/IML matrix language.

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