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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$er
8/18/2019 c02 Lp Models
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Linear Model *ame0 PQR Sol$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
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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
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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$e +unc Side0 *o
Sole !ariables 1 2 8 4 ;
1 !ar" *ame0 P1 P2 P8 P4 P;
1 &alues0 ;9.6 62.68 1.;9 1;.64
Change #elation-ower )ounds0
6 :pper )ounds0
-inear 5'. Coe".0 19 2; 1 12 1;
Constraints
*um. *ame &alue Rel. R 16 1.2 1.8 .7 .;
2 M2 2 => 2 .7 2.2 1.6 .; 1
8 M8 12 => 12 . .7 1.8 1 .9
4 M4 29 => 29 1.4 2.9 .; 1.2 .6
Constraint &alues
Constraint *ames Constraint -imits
Constraint Relationships
8/18/2019 c02 Lp Models
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. 1 /ter.
tal /ter. ;
p. ime 0
Status 5ptimal
&aria'le *ames
Simple -ower )ounds
Simple :pper )ounds
5'ecti$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 ,,,
8/18/2019 c02 Lp Models
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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
8/18/2019 c02 Lp Models
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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
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