Read through this short tutorial to understand the mechanics of the simplex method. Also skim this article for a more intuitive understanding of why the simplex method works/where it fails.
Reading Questions
1) Write an example of a linear program (maximization function, 3 variables, and 3 constraints).
2) Why do we rewrite the constraints with slack variables? What do slack variables represent?
3) Write the initial tableau for your linear program written in question 1.
4) Why do we use the test ratio to choose a pivot row?
5) Why do we want to eliminate the negatives in the objective row?
6) How does the dual relate to the simplex method?
7) How do we prevent the algorithm from cycling?
8) What are some inputs that will cause the simplex method to fail?