Linear Programming - Simplex Applet
By Pedro Miguel Silva and Tiago Castro Guise
Version 1.0 - Lisbon, July 1998, updated on October
1999
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Simplex Applet:
The available LP algorithms are: Simplex Method, Revised Method, Primal
Dual and Simplex Dual.
Enter Your Linear Program:
How the Applet Works:
Buttons:
-
Solve - Solve your linear program.
-
Abort - Abort the execution of the algorithm.
-
Clear - Allows you to clear fields.
-
About - Brings up an about window.
Choice Menus:
-
First Choice Menu - With this options you can chose clear
the field results or clear the field linear program. It is also, available
the options of no clear fields and clear all fields.
-
Second Choice Menu - Chose the algorithm you want Simplex,
Revised Simplex, Primal Dual or Simplex Dual. .
-
Third Choice Menu - Chose output options.
Linear Programming:
A linear program is a problem a problem
that can be expressed as follows:
min
cx (Standard Form)
subject to Ax = b
x >= 0
Where "x" is the vector of variables to be
solved, "A" is the matrix of known coefficients and "c" and "b" are vectors
of known coefficients. The Expression "cx" is called the objective function
and the equations "Ax = b" are called the constraints.
Syntax of Linear Program:
[max:|min:] c1 x1
+ ... + cN xN; (Objective function)
[c1:] a11x1
+ ... + a1NxN "= | > | <
| => | <=" b1; (Constraints)
[cM:] aM1x1 +
... + aMNxN "= | > | < | => | <=" bM;
Where "x" is the vector of variables to be solved
for, "A" is a matrix of known coefficients, and "c" and "b" are vectors
of known coefficients. M is the number of constraints and N is the
number of variables.
A Small Example:
The following example demonstrates the applet. This
problem requires the two phases method.
2 constraints and 2 variables
min: x1 + 1.5 x2;
c1: 0.5 x1 + x2 >= 7.5;
2 x1 + x2 >= 15;
x1 >= 0;
x2 >= 0;
INESC
Instituto de Engenharia de Sistemas e Computadores
Lisbon, Portugal - Europe
ALGOS Group ALGorithms for Optimization
and Simulation
Created by: Pedro
Miguel Silva and Tiago Castro Guise
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