# Simplex method handout

```APPLYING THE SIMPLEX METHOD
TO SOLVE A LINEAR PROGRAMMING PROBLEM
Is the problem in
standard form?
NO
STOP: The basic
simplex method is not
applicable.
YES
Form the initial
simplex tableau
Are there negative
indicators in the last
row to the left of the
P column?
NO
STOP: You have the optimal
solution. Set the nonbasic
variables =0 and assign the basic
variables the values in the last
column.
YES
Choose the pivot column. (If no
positive elements in the pivot
column above the dashed line, the
L.P.P. has no optimal solution.)
Choose the pivot
row.
pivot entry.
Inspect the
simplex tableau
you obtain.
SIDE NOTES:
**STANDARD FORM: 3 conditions must be
met: (1) Objective function is to be
maximized, (2) Variables are all nonnegative,
and (3) the other constraints must be of the
form (linear polynomial)  a where a is a
positive number or zero.
**PIVOT COLUMN: The column that has
the most negative entry in the last row.
**PIVOT ROW: For each row, except the
last one, with a positive entry in the pivot
column, compute the ratio of the number in the
last column to the number in the pivot column.
The pivot row is the row with the smallest
nonnegative ratio. If denominator is 0, no
ratio is formed. If there are 2 or more rows
that have the same ratio, any of these rows may
be selected.
**PIVOTING: Using row operations, change
the pivot entry to 1 and all other entries in the
pivot column to 0.
```