Simplex Method

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Simplex Method

Step Three

perform a pivot operation

perform row operations

the entering row will replace the exiting row

get the pivot element to 1 with everything above and below to a 0

Step Four

If any remaining negative numbers in the bottom row, CIRCLE BACK TO STEP ONE

Step Two

determine pivot element

where the pivot row and pivot column intersect is the pivot element

the variable to the left in the pivot row is the exiting variable

find the pivot row

the smallest quotient determines the pivot row

divide non-negative elements in pivot column by corresponding numbers in the far right row (the "answer" row)

the variable on top of the pivot column becomes the entering variable

look at the bottom row & find largest negative number (this is the pivot column)

Step One

the slack variables and the P variable equaling the solution constant are referred to as a "basic solution"

set up Simplex tableau

this is almost identical to an augmented matrix & manipulation is the same

PreStep

rewrite the objective function

equal everything to zero

P must be positive

use slack variables

one slack variable per equation

rewrite inequalities as equalities

this method ONLY works with less-than-or-equal sign

replace less-than-or-equal sign with equal sign