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Chap 5.4 The Simplex Method for Standard Maximization Problems in Standard Form_2

Chap 5.4 The Simplex Method for Standard Maximization Problems in Standard Form_2

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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 8l-3). 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) ’ _ . How-1mm P: 50 xi +801 Subjed To 1;:l 4kg“ 5 3; 3x) +K[I& 7(\ )KQ >/ O A. Write the Initial System *x‘ + M; +51": 31 433mm 511 "F LIZ; + 3:1 ‘4 8H mammmz '50X| ~ 8023,; + P = O slackmicxbm B. Write the Initial Tableau (m HAWK iv QcToVLWD [2100 108‘! The Simplex Method by Dr. Guillaume Leduc How to Find the Pivot Element and draw a circle-around _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 \ W2. SAMMY cinema 0 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 E N‘l‘fin 3ck XL 905 5( <1 83 P S. ‘\ 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. E ~1‘er 3. Make all the other elements in the Pivot Column equal to zero ENTev‘ 6 xi. IL x5 3—] S '3 P . ’2' I . ‘ ~ R3+Rlfifia ‘5 R3 mean, C. Update the Basic variables on the left of the Tableau ) bum “Er‘li‘ mop knob; 21. ouvfi "E'M‘wu wow 53 $1 1336/) refldflcl 7g The Simplex Method by Dr. Guillaume Leduc ____ _4_—__ mm“ m A; sluiéld—Tgbl—ea“ L—fw ' (D a; m Mvmublfi' an». new been vo’Mfi‘Mb ‘ W4 '1) “q We‘gemus. SJQMfiM ...
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