Simplex Method

rewrite inequalities as equalities

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

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

use slack variables

one slack variable per equation

rewrite the objective function

P must be positive

equal everything to zero

set up Simplex tableau

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

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

determine pivot element

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

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

find the pivot row

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

the smallest quotient determines the pivot row

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

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

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

perform a pivot operation

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

the entering row will replace the exiting row

perform row operations