Unformatted text preview: The Simplex Method by Dr. Guillaume Leduc The QIGX Method {for Standard Maximization Problems in Standard Form! 1. Preparation:
A. Write the initial System B. Write the initial Tableau
2. Find the Pivot Element and draw a circle around it: A. Find the Pivot Column and write “Enter” on top of it o How do you find the Pivot C olunm‘? Go through all the elements in the
last row. Take the most negative one. On top of its column write Enter.
This column is the Pivot Column. 0 What if you cannot ﬁnd the Pivot Column? (It is possible that there is
no negative number in the last row) Stop! You have found the optimal
solution! It is the basic feasible solution you get from the simplex tableau. 3. Find the Pivot Row and write “Exit” to the left of it o How do you ﬁnd the Pivot Row? You have to perform some calculations.
Divide each element ofthe last column by the corresponding element in
the Pivot Column. Ignore any division where the element in the pivot
column is 0 or negative (i.e. ignore anything like 8/0 or 8l3). The Pivot
Row is the row corresponding to the smallest division. II What if you cannot ﬁnd the Pivot Row? (It is possible that there are only
negative numbers in the Pivot Column] Stop! The optimal solution does
not exist C. Draw a circle around the Pivot Element. It is at the
intersection of the Pivot Column and the pivot Row 3. Perform a Pivot Operation:
A. Multiply by a constant to make the pivot element equal to 1 B. Make all the other elements in the Pivot Column equal to
zero C. Update the Basic variables on the left of the Tableau 4. Continue to perform Step 2 followed by Step 3 until
you are forced to stop (either in Step 2.A or 2.3} The Simplex Method by Dr. Guillaume Leduc—WW—w Steg1 Preg' ration (Example) ’ _ .
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108‘! The Simplex Method by Dr. Guillaume Leduc How to Find the Pivot Element and draw a circlearound
_i—t:——————————————. A. Find the Pivot Column and write “Enter” on top of it 0 How do you ﬁnd the Pivot Column? Go through all the elements in the
last row. Take the most negative one. On top of its column write Enter. This column is the Pivot Column. 9 WNV‘Q mm?“
Eniex o What if you cannot ﬁnd the Pivot Column? (It is possible that there is
no negative number in the last row) Stop! You are now able to give the
optimal solution The Simplex Method by Dr. Guillaume Leduc B. Find the Pivot Row and write “Exit” to the left of it o How do you ﬁnd the Pivot Row? You have to perform some calculations.
Divide each element of the last column by the corresponding element in I
the Pivot Column. Ignore any division where the element in the pivot
column is O or negative (i.e. ignore anything like 8/0 or 8/3). The Pivot
Row is the row corresponding to the smallest division. WVWC E x‘d) inevﬂ \DQCW 51\ i0 5 \
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negative numbers in the Pivot Column) Stop! The optimal solution does
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x O The Simplex Method by Dr. Guillaume Leduc Perform a Pivot Ogeration: A. Multiply by a constant to make the pivot equal to 1.
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 Fall '08
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