How to make good simplex method homework problems?

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Has anyone here come across a good method for generating linear programs that are easily solved by hand via the simplex method? Specifically, is there a nice way to ensure that the tableaus don't end up with a lot of messy fractions (or, even better, are all integer?)

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One approach that works in two-dimensions (plus slacks for as many inequality constraints as you might want) is:

  1. On a graph, pick the corners of your feasible region.

  2. Find the equations of lines connecting the corners. Scale the equations so that all coefficients are integers. You can add degenerate constraints at this point if you'd like by picking a vertex and adding some extra inequality constraints.

  3. Add an objective function to suit your needs. For example, you might want multiple optimal solutions.

  4. Compute the dictionary for each possible basis, confirm that the equations don't involve difficult coefficients, and rescale the objective or constraints if necessary to fix any problems.

You can extend this to three dimensions with some difficulty.

I try to get my students using computer algebra systems like Maple (or even a graphing calculator) as soon as possible so that doing the algebra by hand isn't a problem. This also helps to make it clear that the simplex method is about moving variables in/out of the basis and solving the equations rather than being about manipulating numbers in a tableau.