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Instructions

Page 1

•

•

•

•

Sect.1

4

6

Sup.

PQR

PQR_Sens

PQR_S

PQ

PQ_Sens

PQ2

Prod

Res_AlRes_Al_Sens

Mix

Mix_Sens

CarRent

CarRent_Sens

Agg

Agg_Sens

Power

Power_Sens

Chem

Chem_Sens

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Instructions

Page 2

Chapter 2 Examples

Operations Research Models and Methods

Paul A. Jensen and Jonathan F. Bard

Instructions

For cases using the LP/IP Solver you must frst load the Jensen LP/IP Solver.

Linear Programming ModelsA Manufacturing Examplehe Manu"acturing #xample

Sensiti$it% Anal%sis

Sol$ed with #xcel Sol$er

Solution Characteristicshe Manu"acturing #xample in wo &aria'les

Sensiti$it% Anal%sis

he Manu"acturing #xample in wo &aria'les with mar(et constraints explicit

Problem ClassesResource Allocation Pro'lem with ranges identi"ied

Resource Allocation Pro'lemSensiti$it% Anal%sis

)lending or Mixing Pro'lem

Sensiti$it% Anal%sis

Car Rental Pro'lem

Sensiti$it% Anal%sis

Aggregate Planning Pro'lem

Sensiti$it% Anal%sis

*etwor( +low Programming Pro'lem

Sensiti$it% Anal%sis

Chemical Processing Example (Supplement)Chemical Processing #xample

Sensiti$it% Anal%sis

http//!!!.me.ute"as.edu/#$ensen/%&''/computation/unit/mp(add/inde".html

http//!!!.me.ute"as.edu/#$ensen/%&''/methods/unit/linear/su)units/teach/inde".html

 *o use this !or+)oo+, you must frst load the 'ath Programming add-in. See the "cel help fletopic 0)out add-ins )eore continuing.

 *his !or+)oo+ comes !ithout control )uttons. *o ma+e the )uttons choose Add Buttons romthe 'ath Programming menu. *his adds )uttons to all the !or+sheets.hen you are moving a !or+)oo+ to another computer, use the Remove Buttons command.

 *his simplifes opening the !or+)oo+ on the other computer. 3uttons are removed rom all!or+sheets.

http://www.me.utexas.edu/~jensen/ORMM/computation/unit/mp_add/index.htmlhttp://www.me.utexas.edu/~jensen/ORMM/methods/unit/linear/subunits/teach/index.htmlhttp://www.me.utexas.edu/~jensen/ORMM/methods/unit/linear/subunits/teach/index.htmlhttp://www.me.utexas.edu/~jensen/ORMM/computation/unit/mp_add/index.html

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Instructions

Page 4

Add-ins Used

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear#xcel Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$erMath Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

Math Programming , -inear,-P/P Sol$er

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Linear Model   *ame0 PQR Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 7664 Side0 *o

Sole !ariables   1 2 8

1 !ar"   *ame0   P Q R

1 &alues0 91.92 16.86 6

Change #elation-ower )ounds0

6 :pper )ounds0 1 4 6

-inear 5'. Coe".0 4; 6 ;

Constraints

*um. *ame &alue Rel. R 24 2 1 1

2 Mach)   24 => 24 12 29 16

8 MachC   229; => 24 1; 6 16

4 Mach?   164 => 24 1 1;

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. 1 /ter.

tal /ter. 4

p. ime 01

Status 5ptimal

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Sensitiit" Anal"sis for $or%sheet P 

!ariable Anal"sis 'bectie !alue ***

*um. *ame &alue

1 P @@@ )asic 4; 2;.7148 98.8888

2 Q @@@ )asic 6 22.; 98

8 R 6 :pper 1.4;4; ; 8.;4;; ,,,

Constraint Anal"sis

*um. *ame &alue

1 MachA 2B4 :pper 1.2278 2B4 @@@ @@@

2 Mach) 2B4 :pper 1.74; 2B4 2B4 2B2

8 MachC @@@ :pper 2B4 @@@ ,,,

4 Mach? @@@ :pper 2B4 @@@ ,,,

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range

-ower

-imit

Range

:pper

-imit

8/18/2019 c02 Lp Models

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Microsoft Excel +, Sensitiit" #eport$or%sheet .ch/,xls0PS

#eport Created 2323// 442 PM

Adusta'le Cells

5inal #educed 'bectie Allo6able Allo6able

Cell 7ame !alue Cost Coefficient 8ncrease 9ecrease

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Linear Model   *ame0 PQR_S Sol$er0 #xcel Sol$er7664 %pe0 -P1 %pe0 -inear

8 Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 7664 Side0 *o

1 Sole1 !ariables   1 2 8

1 !ar"   *ame0   P Q R

&alues0 91.92 16.86 6

Change #elation-ower )ounds0

:pper )ounds0 1 4 6

-inear 5'. Coe".0 4; 6 ;

Constraints

*um. *ame &alue Rel. R 24 2 1 1

2 Mach)   24 => 24 12 29 16

8 MachC   229; => 24 1; 6 16

4 Mach?   164 => 24 1 1;

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p. ime 06

Status 5ptimal

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Microsoft Excel +, Sensitiit" #eport$or%sheet .ch/,xls/0PS

#eport Created ;3/43/< =24 PM

Adusta'le Cells

5inal #educed 'bectie Allo6able Allo6able

Cell 7ame !alue Cost Coefficient 8ncrease 9ecrease

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Linear Model   *ame0 Q_Ee' Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 68 Side0 *o

Sole !ariables   1 2

1 !ar"   *ame0   P Q

1 &alues0 1 8

Change #elation-ower )ounds0

1 :pper )ounds0 1 ;

-inear 5'. Coe".0 4; 6

Constraints

*um. *ame &alue Rel. R 24 1; 1

2 )   24 => 24 1; 8

8 C   16; => 24 1; ;

4 ?   11; => 24 1 ;

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. 1 /ter.

tal /ter. 8

p. ime 01

Status 5ptimal

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Sensitiit" Anal"sis for $or%sheet P&1$eb

!ariable Anal"sis 'bectie !alue ?@=

*um. *ame &alue

1 P 1 :pper 1; 4; 8 ,,,

2 Q 8 )asic 6

Constraint Anal"sis

*um. *ame &alue

1 A 1B9 )asic 2B4 1B9 ,,,

2 ) 2B4 :pper 2 2B4 1B; 8B

8 C 1B6; )asic 2B4 1B6; ,,,

4 ? 1B1; )asic 2B4 1B1; ,,,

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range

-ower

-imit

Range

:pper

-imit

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Linear Model   *ame0 PQ Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 4664 Side0 *o

Sole !ariables   1 2

1 !ar"   *ame0   P Q

1 &alues0 91.92 16.86

Change #elation-ower )ounds0

6 :pper )ounds0 1 4

-inear 5'. Coe".0 4; 6

Constraints

*um. *ame &alue Rel. R 19 2 1

2 Mach)   144 => 144 12 29

8 MachC   182; => 24 1; 6

4 Mach?   164 => 24 1 1;

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. 1 /ter.

tal /ter. 8

p. ime 0

Status 5ptimal

8/18/2019 c02 Lp Models

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Sensitiit" Anal"sis for $or%sheet P&

!ariable Anal"sis 'bectie !alue ***

*um. *ame &alue

1 P @@@ )asic 4; 2;.7148 12

2 Q @@@ )asic 6 22.; 1;

Constraint Anal"sis

*um. *ame &alue

1 MachA 1B9 :pper 1.2278 1B9 88.8888 @@@

2 Mach) 1B44 :pper 1.74; 1B44 1B9 1B6

8 MachC @@@ )asic 2B4 @@@ ,,,

4 Mach? @@@ )asic 2B4 @@@ ,,,

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range

-ower

-imit

Range

:pper

-imit

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Linear Model   *ame0 PQ2 Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 *o Com

1 5'ecti$e0 4664 Side0 *o

Sole !ariables   1 2

1 !ar"   *ame0   P Q

1 &alues0 91.92 16.86

Change #elation-ower )ounds0

6 :pper )ounds0

-inear 5'. Coe".0 4; 6

Constraints

*um. *ame &alue Rel. R 19 2 1

2 Mach)   144 => 144 12 29

8 MachC   182; => 24 1; 6

4 Mach?   164 => 24 1 1;; Mar_P   91.92 => 1 1

6 Mar_Q   16.86 => 4 1

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. 1 /ter.

tal /ter. 8

p. ime 0

Status 5ptimal

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Linear Model   *ame0 Prod Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 *o Com

1 5'ecti$e0 29 5'ecti$e +unc Side0 *o

Sole !ariables   1 2 8 4 ;

1 !ar"   *ame0   P1 P2 P8 P4 P;

1 &alues0 ;9.6 62.68 1.;9 1;.64

Change #elation-ower )ounds0

6 :pper )ounds0

-inear 5'. Coe".0 19 2; 1 12 1;

Constraints

*um. *ame &alue Rel. R 16 1.2 1.8 .7 .;

2 M2   2 => 2 .7 2.2 1.6 .; 1

8 M8   12 => 12 . .7 1.8 1 .9

4 M4   29 => 29 1.4 2.9 .; 1.2 .6

Constraint &alues

Constraint *ames Constraint -imits

Constraint Relationships

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. 1 /ter.

tal /ter. ;

p. ime 0

Status 5ptimal

&aria'le *ames

Simple -ower )ounds

Simple :pper )ounds

5'ecti$e Coe""icients

Constraint Coe""icients

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Linear Model   *ame0 Mix Sol$er0 ensen -P/P Ph %pe0 -P2 %pe0 -inear o

Change   3oal0 Min Sens.0 es Com

1 5'ecti$e0 4.16 Side0 *o

Sole !ariables   1 2 8

1 !ar"   *ame0   - C S

1 &alues0 .29 .64 .828

-ower )ounds0

6 :pper )ounds0 1 1 1

-inear 5'. Coe".0 1 8.;

Constraints

*um. *ame &alue -ower :pper -inear Constraint Coe""icients

1 Calcium   .12 .9 .12 .89 .1 .2

2 Protein   .22 .22 1 . .;

8 +i'er   .8 .; .2 .9

4 onser$e   1 1 1 1 1 1

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. 1 /ter. 1

tal /ter. 8

p. ime 01

Status 5ptimal

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Sensitiit" Anal"sis for $or%sheet Mix

!ariable Anal"sis 'bectie !alue >+,

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Linear Model   *ame0 Res_Al Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 29 Side0 *o

Sole !ariables   1 2 8 4 ;

1 !ar"   *ame0   P1 P2 P8 P4 P;

1 &alues0 ;9.6 62.68 1.;9 1;.64

Change #elation

6

-inear 5'. Coe".0 19 2; 1 12 1;

Constraints

*um. *ame &alue Rel. R 16 1.2 1.8 .7 .;

2 M2   2 => 2 .7 2.2 1.6 .; 1

8 M8   12 => 12 . .7 1.8 1 .9

4 M4   29 => 29 1.4 2.9 .; 1.2 .6

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. 1 /ter.

tal /ter. ;

p. ime 01

Status 5ptimal

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Sensitiit" Anal"sis for $or%sheet #es1Al

!ariable Anal"sis 'bectie !alue ***

*um. *ame &alue

1 P1 @@@ )asic 19 18.2;;2 24.966

2 P2 @@@ )asic 2; 28.9487 41.91;9

8 P8 -ower ,18.;88 1 ,,, 28.;88

4 P4 @@@ )asic 12 11.2 17.222

; P; @@@ )asic 1; .1 1;.8681

Constraint Anal"sis

*um. *ame &alue

1 M1 16 :pper 4.91; 16 .849; 172.61

2 M2 2 :pper ;.216 2 194.61 28.86868 M8 12 :pper 9.68; 12 11.12 287.;;

4 M4 29 :pper .8681 29 2;.819 2;.6412

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range-ower

-imit

Range:pper

-imit

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Linear Model   *ame0 CarRent Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Min Sens.0 es Com

1 5'ecti$e0 21; Side0 *o

Sole !ariables   1 2 8 4 ; 6

1 !ar"   *ame0   Sat Sun M u E h

1 &alues0 ;

Change #elation-ower )ounds0

6 :pper )ounds0 @@@ @@@ @@@ @@@ 1 1

-inear 5'. Coe".0 8; 8; ; ; ; ;

Constraints

*um. *ame &alue Rel. R 2 1

2 Sun   ; G> ; 1

8 Mon   1 G> 1 1

4 ues   ; G> 8 1 ; Eed   16 G> 16 1

6 hurs   7 G> 7 1

7 +ri   11 G> 11

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. 1 /ter. 7

tal /ter. 1

p. ime 01

Status 5ptimal

7 9 1 11 12 18

+ MuE uEh Eh+ ee(en ee(da Eee(

4 2 ;

1 @@@ @@@ @@@ @@@ @@@ 1

; 12; 12; 12; 6 19 2

1 1

1 1

1 1 1

1 1 1 1 1 1 1 1 1

1 1 1 1

1 1 1 1

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Sensitiit" Anal"sis for $or%sheet Car#ent

!ariable Anal"sis 'bectie !alue /@

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Linear Model   *ame0 Agg Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Min Sens.0 es Com

1 5'ecti$e0 @@@ Side0 *o

Sole !ariables   1 2 8 4 ; 6

1 !ar"   *ame0   P1 P2 P8 P4 P; P6

1 &alues0 18; 14 1 ;; 17 2

Change #elation-ower )ounds0

6 :pper )ounds0 @@@ @@@ @@@ @@@ @@@ @@@

-inear 5'. Coe".0 1 1; 11 11; 11 11

Constraints

*um. *ame &alue Rel. R 18 1

2 M2   14 > 14 1

8 M8   1 > 1 1

4 M4   9 > 9 1 ; M;   17 > 17 1

6 M6   1 > 1 1

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. 1 /ter. 6

tal /ter.

p. ime 01

Status 5ptimal

7 9 1 11 12 18

/ /1 /2 /8 /4 /; /6

2 2; 2; 2; 1

2 1

2 2; 2; 2; 2; 2; 1

4 4 4 4 4 4

1 ,1

1 ,1

1 ,1

1 ,1 1 ,1

1 ,1

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Sensitiit" Anal"sis for $or%sheet Agg

!ariable Anal"sis 'bectie !alue 4??@2

*um. *ame &alue

1 P1 1B8; )asic 1 4 11

2 P2 1B4 )asic 1; 14 16

8 P8 1B )asic 11 1 111

4 P4 ;; )asic 11; 114 ,,,

; P; 1B7 )asic 11 16 11

6 P6 2B )asic 11 114

7 / 2 :pper ,6 4 ,,, 1

9 /1 2; :pper ,1 4 ,,, ;

/2 2; :pper ,1 4 ,,, ;

1 /8 2; :pper ,1 4 ,,, ;

11 /4 -ower 4 ,; ,,,

12 /; -ower 4 4 ,,,18 /6 1 :pper 11 ,,, ,11

Constraint Anal"sis

*um. *ame &alue

1 M1 1B8 Fualit 1 1B8 ,; ,,,

2 M2 1B4 Fualit 1; 1B4 ,,,

8 M8 1B Fualit 11 1B ,,,

4 M4 9 Fualit 11; 9 2; ,,,

; M; 1B7 Fualit 11 1B7 ,,,

6 M6 1B Fualit 11 1B ,1 ,,,

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range

-ower

-imit

Range

:pper

-imit

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Linear Model   *ame0 Power Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Min Sens.0 es Com

1 5'ecti$e0 49818 Side0 *o

Sole !ariables   1 2 8 4 ; 6

1 !ar"   *ame0   PA P) PC xA) xAC x)A

1 &alues0 17.; 1

Change #elation-ower )ounds0

6 :pper )ounds0 1 7; 1 @@@ @@@ @@@

-inear 5'. Coe".0 ; 47; 4

Constraints

*um. *ame &alue Rel. R ,1 1 1 ,.;

2 )   > ,1 ,.; 1

8 C   @@@ > ,1 ,.;

4 H   ,2; > ,2; ;   ,; > ,;

6 I   ,8 > ,8

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. 1 /ter. 6

tal /ter. 1

p. ime 01

Status 5ptimal

7 9 1 11 12 18 14 1;

x)C xCA xC) %AH %AI %) %)I %CH %C

16.67 1;.98 17.; 27.79 ;;.;6

@@@ @@@ @@@ @@@ @@@ @@@ @@@ @@@ @@@

,.; 1 1

1 ,.; 1 1

,.; 1 1 1 1

,. ,. ,. ,.

,. ,.

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Sensitiit" Anal"sis for $or%sheet Po6er

!ariable Anal"sis 'bectie !alue >4@=

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Linear Model   *ame0 Chem Sol$er0 ensen -P/P Ph1 %pe0 -P2 %pe0 -inear o

Change   3oal0 Max Sens.0 es Com

1 5'ecti$e0 @@@ Side0 *o

Sole !ariables   1 2 8 4 ; 6

1 !ar"   *ame0   A ) C M1 AM1 )M1

1 &alues0 ; 1671 7148 1;49 8;7.1

-ower )ounds0

6 :pper )ounds0 @@@ ; @@@ 1 @@@ @@@

-inear 5'. Coe".0 ,4 ,8 ,1

Constraints

*um. *ame &alue -ower :pper -inear Constraint Coe""icients

1 A_C5*   1 ,1

2 )_C5*   @@@ 1 ,1

8 C_C5*   1

4 1_C5*   @@@ ,1 1 1; 1_C5* 8#,12 1

6 2_C5*  

7 2_C5* #,12

9 H_C5*  

_C5* ;#,12

1 I_C5*  

11 )_C5*  

12 AM1J   988.8 @@@ ,.1 1

18 )M1J   @@@ @@@ ,.; 1

14 )M2J  

1; HM1J   @@@ ,.7

16 MJ   @@@ ,.2 17 M2J  

19 IM2J   @@@

1 I-/M   296 1 @@@

2 Con 2   ; @@@ 1 1

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. 1 /ter. 22

tal /ter. 24

p. ime 02

Status 5ptimal

7 9 1 11 12 18 14 1; 16 17 19

CM1 HM1 M1 EM1 M2 )M2 CM2 M2 IM2 A5M2 H

;289 ; 142 714.8 1;476 4648 1988 4648 296 1;49 ; 671

@@@ @@@ @@@ @@@ @@@ @@@ @@@ @@@ @@@ @@@ ; @@@

;

1

,1

,1 ,1

1 ,1 ,1 ,1

,1 1 1

1 ,1 ,1 ,1

1 ,1

1 1 ,1

1

1

,.8 1

1

1 ,.8 1

,.6 1

8/18/2019 c02 Lp Models

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1 2 21

I 1 2

296 ; ;;71

@@@ ; @@@

1 11 9

,1

,1 ,1

1

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Sensitiit" Anal"sis for $or%sheet Chem

!ariable Anal"sis 'bectie !alue ***

*um. *ame &alue

1 A -ower ,8 ,4 ,,, ,1

2 ) ;B :pper 28 ,8 ,26 ,,,

8 C @@@ )asic ,1 ,4 ,,,

4 M1 @@@ )asic ,2.9; ,,,

; AM1 @@@ )asic ,6 8

6 )M1 @@@ )asic ,;7 2;

7 CM1 @@@ )asic ,2.498 6

9 HM1 ;B )asic ,4.714 ,,,

M1 @@@ )asic ,14.2; ,,,

1 EM1 @@@ )asic ,29.; ,,,

11 M2 @@@ )asic ,6. 17.1

12 )M2 @@@ )asic ,28 ;718 CM2 @@@ )asic ,.9;71 24.4296

14 M2 @@@ )asic ,28 ;7

1; IM2 @@@ )asic ,11.; 29.;

16 A5M2 @@@ )asic ,6 171

17 H ;B :pper 4.714 ; .296 ,,,

19 @@@ )asic ,1 ,,,

1 I @@@ )asic 1 ,1.; 89.;

2 1 ; :pper 8 11 9 ,,,

21 2 @@@ )asic 9 ,11 11

Constraint Anal"sis

*um. *ame &alue

1 _C5* Fualit ,1 @@@ 988.8888

2 _C5* Fualit ,26 @@@ 2B;

8 _C5* Fualit ,1 @@@ ,,,

4 1_C5 Fualit ,1 @@@ ,,,

; 1_C5* Fualit ,,, 714.29;7

6 2_C5 Fualit ,1 @@@ ,,,

7 2_C5* Fualit ,1 @@@ 988.8888

9 _C5* Fualit ,.296 @@@ 2B

_C5* Fualit ,9 ,,, @@@

1 _C5* Fualit ,1 ,,, @@@

11 )_C5 Fualit ,9 ,,, @@@

12 AM1J @@@ )asic ,,, 988.8888

18 )M1J -ower ,2; ,8;7.142 2B;

14 )M2J Fualit ,2; @@@ 2B;

1; HM1J Fualit .296 ,2B 62;

16 MJ Fualit 9 @@@ 714.29;7

17 M2J Fualit 7 @@@ 988.8888

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Statu

s

Shadow

Price

Constraint

-imit

Range-ower

-imit

Range:pper

-imit

8/18/2019 c02 Lp Models

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19 IM2J Fualit @@@ 988.8888

1 I-/M @@@ )asic 1B ,,, @@@

2 on 2;B )asic 1B ;B ,,,

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Sensitiit" Anal"sis for $or%sheet us

!ariable Anal"sis 'bectie !alue /?

*um. *ame &alue

1 x 4 )asic 1 1

2 x4 1 )asic 1 1

8 x9 -ower 1 1 ,,,

4 x12 9 )asic 1 1 1

; x16 4 )asic 1 1 1

6 x2 -ower 1 1 ,,,

Constraint Anal"sis

*um. *ame &alue

1 ? 4 -ower 1 4 ,,,2 ?4 14 )asic 9 ,,, 14

8 ?9 1 -ower 1 1 4 ,,,

4 ?12 9 )asic 7 ,,, 9

; ?16 12 -ower 1 12 11 ,,,

6 ?2 4 -ower 4 ;

Statu

s

Reduced

Cost

5'ecti$e

Coe""icient

Range

-ower

-imit

Range

:pper

-imit

Status

ShadowPrice

Constraint-imit

Range

-ower-imit

Range

:pper-imit

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Linear Model   *ame0 )us Sol$er0 ensen -P/P Ph1 %pe0 -P1 %pe0 -inear o

Change   3oal0 Min Sens.0 es Com

1 5'ecti$e0 26 Side0 *o

Sole !ariables   1 2 8 4 ; 6

1 !ar"   *ame0   x x4 x9 x12 x16 x2

1 &alues0 4 1 9 4

Change #elation

6

-inear 5'. Coe".0 1 1 1 1 1 1

Constraints

*um. *ame &alue Rel. R 4 1 1

2 ?4   14 G> 9 1 1

8 ?9   1 G> 1 1 1

4 ?12   9 G> 7 1 1 ; ?16   12 G> 12 1 1

6 ?2   4 G> 4 1 1

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. 1 /ter. 7

tal /ter. 7

p. ime 0

Status 5ptimal

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Linear Model   *ame0 ist1_-P Sol$er0 ensen -P/P Ph. 1 /ter.1 %pe0 -P1 %pe0 -inear otal /ter.

Change   3oal0 Min Sens.0 *o Comp. ime

1 5'ecti$e0 ;8 Side0 *o Status

Sole !ariables   1 2 8 4 ; 6 7

1 !ar" *ame0

1 &alues0 2 2 2 1 ;

Change #elation-ower )ounds0

6 :pper )ounds0 2 2 2 2 2 2 2

-inear 5'. Coe".0 6 8 8 7 ; 4 6

Constraints

*um. *ame &alue Rel. R 7 1 1 1 1

2 Chi   ,2 > ,2 ,1 ,1

8 -A   ,2 > ,2 ,1 ,1 4 ?al   ,8 > ,8 ,1 1 1 1

; Atl   ,1; > ,1; ,1

6 *   ,2; > ,2; ,1

7 Aus   2 > 2

9 3ain   2 > 2

Phoe,

Chi

Phoe,

-A

Phoe,

?al

Phoe,

Atl

?al,

-A

?al,

Chi

?al,

*

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12

17

@@@

5ptimal

9 1 11 12 18 14 1; 16 17

; 2 2

2 2 2 2 2 2 2 2 2 2

2 ; 2 4 7 2 ; 6 4 7

,1

,1 1 ,1 ,1 ,1

,1 1 1 1 ,1 ,1

,1 ,1

1 1 1

1 1 1

?al,

Atl

Atl,

*

Atl,

?al

Atl,

Chi

Aus,

-A

Aus,

?al

Aus,

Atl

3ain,

?al

3ain,

Atl

3ain,

*

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7et6or% Model   *ame0 ?ist1 Sol$er0 ensen *etwor1 %pe0 *et %pe0 -inear

Change   3oal0 Min Sens.0 *o

1 5'ecti$e0 ;8 Side0 *o

Sole

1 !ar"1 Arc 9ata and 5lo6s

*um. *ame +low 5rigin erm. -ower :pper Cost 3ain +low_5

6   1 hoe,Ch   2 1 2 2 6 1 2

  2 hoe,-   2 1 8 2 8 1 2

  8 hoe,?a   2 1 4 2 8 1 2

  4 hoe,Atl   1 1 ; 2 7 1 1

; ?al,-A   4 8 2 ; 1

6 ?al,Chi   4 2 2 4 1

7 ?al,*   ; 4 6 2 6 1 ;

9 ?al,Atl   ; 4 ; 2 2 1 ;

Atl,*   ; 6 2 ; 1 1 Atl,?al   ; 4 2 2 1

11 Atl,Chi   ; 2 2 4 1

12 Aus,-A   7 8 2 7 1

18 Aus,?al   2 7 4 2 2 1 2

14 Aus,Atl   7 ; 2 ; 1

1; ain,?a   9 4 2 6 1

16 3ain,Atl   9 ; 2 4 1

17 3ain,*   2 9 6 2 7 1 2

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Ph. 1 /ter. 2

otal /ter. 11

Comp. ime 01

Status 5ptimal

7ode 9ata and alance Constraints

*um. *ame +ixed )alance

1 Phoe   7

2 Chi   ,2

8 -A   ,2

4 ?al   ,8

; Atl   ,1;

6 *   ,2;

7 Aus   2

9 3ain   2