lecture - 7 overview of or , lpp graphical , simplex

8/6/2019 Lecture - 7 Overview of or , LPP Graphical , Simplex

1/68

$08843

39073,880882039

$97:.9:70

%072

$9,989.8#

$08843

!7,.9.0$0098

8.:8843,3/$,250

$0,.:,943

$08843

,70$,2508 147

545:,94357454794307.803974/:.943944309,0/9089

$08843

$9,989.,310703.0 $,253

,70$,2508

549088%0893 %4

%,0/%0898

431/03.03907;,

4770,943$.,9907

/,7,230,7

/0503/03.0

!0,78438

.4770,943

.4011.039

$08843

,:80110.9#0708843

!,7,20907841#0708843

4011.03941090723,943

$08843

07.80,3/57,.9.08009

/8.:8843

$08843

;07;041# !!

472:,943,3/7,5.,2094/

$088439.79.,;,:0814720,3

55742,94341342,-

3472,07.80

$250094/:,

!74-028

39073,880882039

88320394/0$:3$7

%7,385479,9434/0

$:3$7

3;0394743974

09473,88!#%

!

$:3$7


2/68

5;16931##

507,9438#080,7.

#96.15.9

!74;/087,943,-,88147/0.8432,3


3/68

08843!,3

5;16931##

;07;041507,9438#080,7. $9058943,88 3974/:.94394!! 55.,9438 7,5.,094/4184;3!! 472:,94341!! ,2508

07.808


4/68

507,9438#080,7.

8.0391.,5574,.94/0.8432,3.800894/09072304-08994/083,3/4507,90,88902:8:,:3/07.43/9438706:7390,4.,943418.,7.07084:7.08


5/68

507,943#080,7.0.843,3

,3,07,/0.8432,38,574.088-.2,3,02039031,.0/9,574-02.44808,850.1..4:78041,.9431742,809415488-045943832,3,/0.843,-:830882,3,07,9902598

94.4480,.4:78041,.9439,9824890110.9;03

90;03.7.:289,3.083,99,33904,8419047,38,943


6/68

:3.943841507,9438#080,7.

$4;089095041.4250574-0289,99:73:539024/073-:8308803;7432039

:/82,902,9.,,3/.425:90724/084147,3,943,889028.425480/41504502,.308,3/574.0/:708

&808,3,9.,,3/3:207.,90.36:08942,0

570/.9438,3//0.8438-,80/43908024/08


7/68

507,9438#080,7.9078.5308

7,8:543

03300732,3,020392,902,9.8

48070,90/9490/0.8438.03.08

,550/2,902,9.8.425:9078.03.00.4342.83/:897,0330073,3/8890280330073


8/68

%0$0;03$905894,44/#3,88

00/-,.4458

,9,0;08


9/68

$:..0881:#55.,9438

425,3 0,7 !74-02 %0.36:08&80/ 33:,$,;38

0099 !,.,7/ 0833-:11078394574/:.943

30":0:324/08 243

%,.40 254008.0/:3 !470.,893$2:,943 243

!74.947,2-0 #0/083574/:.943/897-:943

88902%7,385479,94324/08 243

09,7308 88335,3089474:908 39007!747,223 243

%% ,. 03907/083 ":0:324/08$2:,943

243

04709$89028

3. 08397:.330947

094724/08

470.,893$2:,943243

$,37,3.8.4!4.0

059 !,974$. 0/:3 30,7!747,223 243

09002$900 083,33494/$975507 39 007 !747,223 2 43

479207.,3',3

308 88334,/894/7;078 094724/03 243

9 4 !09 740:2 #013074507,9438/897-:94330,7!747,223

470.,893243

&390/7308 $.0/:370807;,94350784330 !":0:3470.,893 243

,72,3870,207 592,574/:.9430;08 30,7!747,223

!58!09740:2 6:52039705,.02039 094724/03


10/68

,902,9.,90.36:0

49.425:9075747,223

4.,9088.,7.07084:7.0894,.0;0,34-0.9;0

!430070/-0470,39347/,7

0;0450/47,-084:943.,0/$250

094/3

,9830,7!747,223


11/68

3974/:.9439430,7!747,223

%025479,3.04130,7!747,223

,370,47/574-02803/90280;089430,7

5747,22324/03 ,370,47/574-028.,3-0,55742,90/-

30,724/08

%070,7003438:..0881:,55.,94383

,3:1,.9:73$.,7.0#084:7.08

,7093!74/:.9-,80/43:/09

3,3.03;089203932:2.489

3/2,32470


12/68

$.0/:38.44-:8808942320 949,/89,3.097,;00/03.,77389:/0398

4.,9354.05,974:39894.720,70,8347/07942320 7085438092094.,8

$.0/:390078,9-,38949,9300/8,70209/:730,.4:74190/,0232390

949,.48941,-47

,250841$:..0881:!55.,9438


13/68

,250841$:..0881:!55.,9438

4393:0/

!.3-03/8417,2,907,83100/2894574/:.01380/100/.42-3,9438,9232:2.4898

$00.9390574/:.923,1,.947942,0-089:80412,.30 ,3/,-474:78,;,,-002,2390172857419

4.,9385,.0147,903,3923,3084553

2,84,8942,2070;03:0894900,83.425,3


14/68

#06:702039841,30,7!747,223

!74-02

:89800942,2047232084206:,399904-0.9;01:3.943

!70803.04170897.943847.43897,398 298,-994,.0;04-0.9;0

:89-0,9073,9;0.4:780841,.9431742.94.4480

-0.9;08,3/.43897,3982:89-0057088-0,830,706:,943847306:,908


15/68

094/84184;3,3!!

7,5.,094/

$250094/ &83.0$4;07

5;16931##


16/68

,2507,5.,094/

,2,943!74-02

,

8:-94


17/68

5;16931##

,2507,5.,$4:943

43897,397,50/


18/68

5;16931##

,2507,5.,$4:943

43897,397,50/


19/68

5;16931##

,2507,5.,$4:943

43897,397,50/


20/68

5;16931##

,2507,5.,$4:943

42-30/43897,397,5


21/68

5;16931##

,2507,5.,$4:943

0,8-0$4:943#043

0,8-00,8-0

#043#043


22/68

5;16931##

,2507,5.,$4:943

-0.9;0:3.94330

-0.9;0:3.943-0.9;0:3.943 -0.9;0:3.943-0.9;0:3.943


23/68

97020!4398,3/90592,$4:943

%0.47307847;079.08419010,8-07043,707010770/94,89009702054398

34592,84:94394,3!574-02.,3-014:3/,9,30970205439419010,8-07043

03443147904592,84:9434:/4349,;0940;,:,90,10,8-084:94354398

4:,;094.438/07439009702054398419010,8-0

7043


24/68

$90583472:,93

!!74-028

0130904-0.9;023472,

013090/0.843;,7,-085489;0

790902,902,9.,1:3.943147904-0.9;0790, 4747//08.75943410,..43897,39

7909079,3/8/0#$410,..43897,39

79047 1470,..43897,39

79090/0.843;,7,-0843$410,..43897,39

79090.4011.0391470,./0.843;,7,-030,..43897,39


25/68

5;16931##

,2507,5.,$4:943

%0;097020!4398

0,8-00,8-0#043#043


26/68

#0.433!!74-028

,7,.90789.841!!74-028

0/0130/8304-0.9;02:89-089,90/

%0702:89-0,9073,9;0.4:780841,.943 %0949,,.0;0203941904-0.9;02:89-0.43897,30/-

8.,7.07084:7.0847490770897,398

%04-0.9;0,3/0,.4190.43897,3982:89-00570880/,830,72,902,9.,1:3.9438


27/68

,25025.0425.083974/:.39430909-..017,208900:0,3/90!74108843,94-02,/01742850.,,:23:2,3/8900,48%0,39.5,90/:39574198,70

147900:0,3/14790!74108843,%03:2-074154:3/8410,.,4300/0/50717,2088:22,70/-048:5507/0;07854:3/84190,:23:2,4,3/54:3/841908900,400

:23:24 $90040:0 !74108843,

42,30:0,3/!74108843,17,20884:/25.574/:.00,.00

5;16931##


28/68

,25025.04 4/0472:,943

'07-,$9,9020394190-0.9;0:3.943

,20949,0057419

'07-,$9,902039419043897,398

%49,00:8,041,:23:2,4 54:3/8

%49,00:8,0418900,4 54:3/8

01394341900.843',7,-08

3:2-07410:017,208574/:.0/00

3:2-0741!74108843,17,208574/:.0/00


29/68

,25025.04

4/0472:,943.4393:0/

, %49,00!7419

8:-94 :23:2;,,-0

$900;,,-0


30/68

,25025.04 592,$4:943

..47/394904:95:9

0:017,208

!74108843,17,208

-0.9;01:3.943;,:0


31/68

,250

47547,9435,3894574/:.094574/:.98,3/.-089470/3,8947,0,70,480.,5,.98861009!74/:.99,088610094185,.0507:39!74/:.9706:70886100999,08

2,.304:78942,3:1,.9:70,:3941!74/:.902,.304:78,70706:70/147,:3941!74/:.9

:7390574/:.9435074/2,.304:78,70,;,,-084,;,,-0,705078434:78147138390574/:.9,3/,:3941574/:.99,082,34:7814713839,:3941 574/:.9300/32,34:78

!7419.4397-:9438,70#8507:3941574/:.9,3/#8507:3941574/:.9347/07942,209057419147905074/42,3:398410,.574/:.984:/-0574/:.0/

5;16931##


32/68

,25032,943!74-02

!472:,943

3

89


33/68

,2507,5.,$4:943

7,59043897,398

43897,3903 903 03 903 4330.9,3/%08/08 ,-4;09830

43897,3903 903 :980993 94 0/ .834943907,5 %:89409,80.43/5439439830809 94,3 3:2-07,7079,3,3/84;014703 903 4330.9,3/%08/08 949079

43897,3903 903 03 903 4330.9,3/%08/08 ,-4;09830


34/68

,2507,5.,$4:943

43897,3987,50/

0,8-0#0430,8-0#043


35/68

$4;01479097020!439,990390780.9434190%43/343897,398

//390809406:,9438;08

47

$:-899:9398394 ;08

,2507,5.,$4:943


36/68

,2507,5.,$4:943

$4;014790592,',:04190-0.9;0:3.943

$4;0147

%:8904592,84:9438


37/68

,2507,5.,$4:943

592,$4:943

33

33

592,592,

592,592,


38/68

4:70,3,3,89147,/;843414/,.2,08.447.02.,890,89943841,3/,90,89943841.4472:89-0

2,/00,.2439%0949,.02.,82,/02:89-0,90,89943842,39438410,..02.,84:/-02,/0942320

.4898

2,3:1,.9:73.4895072439

4472,3:1,.9:73.4895072439

470475

,250


39/68

0.843;,7,-08

943841.02.,574/:.0/

943841.447.02.,574/:.0/

-0.9;0

320 43897,398

K K447

K%49,9433,0 K K 4330,9;9

,250


40/68

,250

0,8-0

#043

%438

447

02.,

%438

447

02.,

%43802.,

447

%49,

3/;,:08147

K

K K


41/68

,250592,$4:943

0,8-0#043

%438

44702.,

%438

44702.,

%43802.,

447

%49,

3/.4730754398


42/68

,250592,$4:943

0,8-0

7043

,

-


43/68

,250310,8-0!74-02

$4;07,5.,147904592,84:943

,

89


44/68

,250310,8-0!74-02

%070,7034543989,98,981-49.43897,39803.098

574-02,83410,8-07043,3/344592,84:943


45/68

,250&3-4:3/0/!74-02

$4;07,5.,147904592,84:943

,

89


46/68

,250&3-4:3/0/!74-02 %010,8-070438:3-4:3/0/,3/904-0.9;01:3.94330.,3-0

24;0/5,7,094980194:9-4:3/849,9 .,3-03.70,80/31390

,,


47/68

30,7!747,22355.,9438

03/3!74-02

!479144!,333!74-02 !74/:.9!74-02

%7,385479,943!74-02

,9,3;04520393,88


48/68

03/3!74-02

70/07.800/425,370.0;0814:77,7,381742

.9-03/898/7509144/%0509144/,/;0798089,9

0,.4:3.0.,32009890232:2/,706:7020398147;9,23574903,3/743%0.489410,.7,7,3,80,890;9,23574903,3/743:39850754:3/410,.7,3,708:22,70/43903098/0

70/07.8839070890/3574/:.3904:3.029:70,9232:2.48902009390232:2/,706:7020398

41:39841;9,23:39841574903,3/:39841743


49/68

03/3!74-02

'9,23!749037437,3&398-&398-&398-489-


50/68

03/3!74-02

013090/0.843;,7,-08

9054:3/8417,3:80/3904:3.029:70

0130904-0.9;01:3.943

32090949,.489147,34:3.029:70


51/68

03/3!74-02

013090.43897,398

%49,094190284:3.0854:3/8

%49,,24:3941'9,2339028,90,89:398

%49,,24:394157490339028,90,89:398

%49,,24:394174339028,90,89:398

4330,9;941;,7,-08 147,


52/68

:,9

;07!!,8,/:,90;03!!8572,

1572,8,2,574-0290/:,8,23574-02

32;,7,-03.43897,39572,,8,33;,7,-02.43897,39/:,

%0/:,84-9,30/-97,3854839097002,97.083;4;0/390572,574-02


53/68

:,9

01470793/:,147,3!!2,08:70

;,7,-08,7034330,9;0

.43897,398,70^950147,2,574-02_950147,23574-02


54/68

!72,/:,#0,94385

88:23,2,572,574-02!72,

,

441;,7,-08

441.43897,398 ^ 950.43897,39

950.43897,39

&370897.90/;,7,-0

-0.9;01:3.943;,:01479;,7,-0

#$.4389,391479.43897,39 4011.039,1479;,7,-0

3909.43897,39

:, 3

441.43897,398

441;,7,-08 4330,9;0;,7,-0

&370897.90/;,7,-0

950.43897,39

#$.4389,391479.43897,39

-0.9;01:3.943;,:01479;,7,-0

4011.039,1479;,7,-03909.43897,39


55/68

!72,/:,#0,94385

110,8-084:9438089147-49572,,3//:,904-0.9;01:3.943;,:08419074592,84:9438,70

06:, %084:9439490/:,.,3-070,/174290

;,:0841908,.8:75:8;,7,-083904592,84:9439,-0,:4190572,

1572,,8:3-4:3/0/84:94390/:,,834

10,8-084:943


56/68

.4342.39075709,94341:,

%0 ;,:08.47708543/3948,.8:75:8;,7,-083904592,84:9433/.,902,73,

57419,-9478,/457.0841907084:7.0890705708039

7084:7.0:3:80/1:,80748,/457.0

:39.,30390,;,,-941,7084:7.0.,308904-0.9;01:3.943;,:0-,3,24:3941

988,/457.0


57/68

$250094/

5;16931##


58/68

,250 ,.947574/:.089700/1107039574/:.98,3/9057419507

:3941.,70,3/70850.9;0%0574/:.98,70574.0880/397004507,9438,3/,3/90920706:70/30,.4507,9431470,.:398;03,8

!74/:.98507,943

%01,.947478/,83,24394:78,/,3948198 %00110.9;047341,90574.08808843/:094,883,-0.,:80805407.:9,3/-70,/43412,.308%01,.947,82,.30834507,9432,.30834507,943,3/4302,.3034507,9433/904592:2574/:.92147902439

5;16931##


59/68

$4:943

5;16931##


60/68

$4:943.439

5;16931##


61/68

$4:943.439/

5;16931##


62/68

,250 !,72,.0:9.,.425,3,8412,907,412,907,,3/

412,907,,;,,-05072439%0.,3:8090802,907,8942,09700-,8.5,72,.0:9.,574/:.983,20,3/070903:2-07830,..,8070570803990-09412,907,2,907,,3/2,907,70850.9;030,.4190574/:.98,3/-,,3.0

70570803983079370/0398%

0.489417,2,907,8;03-04370/039 489507

,9

,9

,9

3079370/039

$!419080574/:.988#8,3/#8,3/#850770850.9;0%0708,.,5,.970897.9434190.425,314790574/:.99,9890.,3349574/:.024709,35072439472:,90,3!!1472,28390243957419

090723042:.410,.4190574/:.9884:/90574/:.0347/07942,2809072439574198

5;16931##


63/68

$4:943.439/

5;16931##


64/68

$4:943.439/

5;16931##


65/68

$4:943.439/

5;16931##


66/68

$4:943.439/

5;16931##


67/68

#0.,5 ;07;041507,9438#080,7.

$9058943,88

3974/:.94394!!

55.,9438

7,5.,094/4184;3!! ,2,94332,943

310,8-0:3-4:3/0/,3//00307,90574-028

,250431472:,94341!!03/3

:,41,3!! $250094/

,2508

07.808

5;16931##


68/68

"

3":0708

lecture - 7 overview of or , lpp graphical , simplex

Documents