## The Simplex Program

**What it teaches:**

This program teaches the Simplex Method of solving linear programming problems.
It shows (1) how to *set up* a maximization or a minimization problem and (2) how to *solve*
the problem using Gaussian elimination. The program allows you to focus on the method and not get bogged
down by the arithmetic. At every point in the procedure the status bar at the bottom of the window offers
context-sensitive help on what to do next.

**How it works:**

Step 1. Set up the initial tableau. The program asks you some general questions such as whether you want to maximize or minimize, how many variables appear in the constraints and how many and of what type are the constraints:

This is enough information to create a tableau of the right size and to partially fill it in:

You finish setting up the tableau by filling in the names of the variables and the constraint coefficients.

Step 2. Apply the Simplex Method. You repeatedly select entering columns and leaving rows with the click of the mouse. The status bar display helps you choose. The Gaussian elimination arithmetic is done by the program — you get to concentrate on the method. Here is the display at the point where the user has to pick an entering variable:

Also, you can save a simplex problem to a file, you can specify the number of significant
figures to be displayed and
you can print a report showing the steps that were used to solve the problem.

**Some ideas for teachers:**

- This application provides a good example of how systems of equations arise in economics.
- Using this program you can create more realistic problems that have more than just one or two constraints.

**Where to now?**