The Simplex Method

Tutoring on The Simplex Method

Learning Objectives:

Understand the Simplex Method.

Math Tutoring on How to use Simplex Method in Standard Maximization

The Simplex method for Standard Maximization problems are as follows:

1. Convert the system of inequalities or constraints to equations using slack variables.

2. Set the objective functions equal to zero. 

3. Create a simplex table and label the active or basic variables.

4. Select the pivot column. This is the column with the most negative numbers on the left side of the bottom row.

5. Select the pivot row Divide each entry in the constant Column by the corresponding positive entry in the pivot column. The smallest positive ratio indicates the pivot row.

6. Select the pivot, which is the entry in pivot column and pivot row. The pivot must be positive. It can’t be zero. Identify the new active material.

7. Perform row operations to make the pivot equal to 1 and the remaining elements in the pivot column equal to zero. Making the pivot equal to 1 is optional.

8. Repeat the process by identifying the most negative entry on the left side of the last row.

9. Once the left side of the last row is all nonnegative, the solution can be found. The value of each row variables or active variables is equal to the right most entry in the row. All inactive variables equal zero.

 

 

 

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Hook Questions:

1.    What is a slack variable?

2.    How to create a simplex table?

3.    What is the difference between pivot row and pivot column?  

 

 

 

 

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