The Simplex Method

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Determine if there are positive elements in the pivot column above the dashed line

YES

Select the pivot element and perform the pivot operation

The goal is to get the pivot element to 1 and everything above and below to 0.

REPEAT UNTIL SOLITION IS FOUND

Read the Basic solution by locating the "1" with the corresponding variable and answer

Meaning there are no negatives in the bottom row

NO

No Solution

The Simplex Method

Rewrite the system of inequalities and the objective function as a system of equalities using slack variables. Set up the Simplex Tableau

Determine the Pivot element: Are there any negatives?

YES, NEGATIVES

Select Pivot Column: Look at the bottom row and find the largest negative number. This becomes the pivot column.

The variable on top of this column becomes the ENTERING variable

Find the Pivot Row: divide the non-negative elements in the corresponding pivot column by the corresponding answer on the right. The smallest number is the pivot row.

The variable to the left of the row becomes the EXITING variable which will replace the ENTERING variable

NO NEGATIVES

Stop! Solution is found!