Row Operations
| Question: Can you guide me through row operations in a simplex method problem? |
Yours
Truly answers: Sure. In the simplex method, only two of the three row operations are normally used:
| • |
Multiply a row by a non-zero number |
| • |
Multiply a row by a non-zero number and add the result to another row |
| |
(The original row DOSE NOT change) |
Let’s look at the following simplex method problem:
| Minimize C = 10x + y subject to |
 |
The dual problem will produce the following initial tableau, on which we will perform row operations:
Here is how to perform necessary row operations:
| Step 1 |
Define matrix A a 3x7 matrix. Then, identify pivot column & row, hence the pivot element. |
| |
|
| |
 |
| |
|
| Step 2 |
R1+(–4)R2 is done by *row+(–4, [A], 2, 1). Store the result into matrix B. |
| |
R2 DOES NOT change! |
| |
|
| |
 |
| |
|
| Step 3 |
R3+(16)R2 is done by *row+(16, [B], 2, 3). Store the result into matrix C. |
| |
R2 DOES NOT change! |
| |
|
| |
 |
| |
|
| Step 4 |
R3+(2)R1 is done by *row+(2, [C], 1, 3 ) |
| |
R1 DOES NOT change! |
| |
|
| |
 |
| |
|
| Step 5 |
Fundamental Theorem of Duality |
| |
This theorem guarantees that the max value obtained above coincides with the min value sought in the original problem. |
| |
Pmax = Cmin = 28 when x = 2 and y = 8 |
|
|
