Online Exercises

Simplex Method---Degenerate Problems

Below is a java applet that will present a set of degenerate linear programming problems for you to solve. You're job is to solve each problem (either by finding an optimal solution or demonstrating that the problem is unbounded). After correctly solving a problem, the applet will immediately give you a new one. After you have solved all the problems in the set, make a screen print of the applet window and email that to your instructor.

In this applet, e1, e2, e3, e4 are the epsilons explained in Chapter 3. In order to figure out which variables leave the basis, you need to remember that the epsilons are part of the current basic variable values and that e1 >> e2 >> e3 >> e4.

Each problem must be solved using the Simplex Method. Any attempt to make an incorrect pivot will be rejected but your score will be increased by one. Low scores are better than high scores.

The set of linear programming problems to be solved is determined by specifying the number of rows, the number of columns, the seed, and the number of problems in the set. Your instructor will tell you what values to use for these fields. Make sure that you enter exactly what your instructor tells you for otherwise you will be doing the wrong set of problems and it will be impossible to fairly evaluate your performance.

When you are ready to begin, press the Go Pivoting button and then, when the pivot window pops up, press the Start button.

Don't forget that incorrectly pressing one of the termination buttons (Optimal or Unbounded) counts as an extra pivot, so press these buttons only when you are confident that it is the correct thing to do.

Final note: if for any reason you wish to start over, you may press the Exit button to quit the exam. At that point you can start afresh. Of course, at some time before this online assignment is due you must go to the end and submit a score.

Bugs. This applet works fine when accessed via Netscape3 on most UNIX workstations and it works fine with either Netscape4 or InternetExplorer4 on WindowsNT. Most other browser/platform combinations do not work correctly. The problem seems to be due to bugs in the browser's JAVA interpreter as implemented on the given platform. If you have trouble getting the applet to behave as described above, try finding a different browser/platform combination.