b4 or assignment ashish

8/12/2019 B4 or Assignment Ashish

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A ComprehensiveReport onTransportationProblem ofSuppliers to itsDistributors

PGDM (BM)

BATCH OF 2013-2015


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GROUP B4 SECTION B PGDM (BM) 2013-15

Letter of Transmitta

This report was prepared as part of Operations Research project assigned by

Professor (Dr) Sambit Mukherjee to the batch of P DM !"#$%!"#& at 'a ier nstitute of

Management* +hubaneswar, The objecti e of this report is so- ing a prob-em scenario using

the techni.ues of formu-ating transportation prob-em using the concepts of -inear

programming using / 0 O,

1e thank Professor (Dr) Sambit Mukherjee for gi ing us this opportunity to -earn

-inear programming* how to formu-ate the prob-em constraints and so- e the prob-em, The

scope of this report is entire-y academic in nature and the situation considered in entire-y

hypothetica-, P-ease fee- free to contact any of the undersigned in case of any .ueries,

!o "#m$er "ame P%one "#m$er&1130'3 2bhina( Prakash %&1130' 2mit Shuk-a %&1130 2 2nshuk Pradhan %&1130 * 2nurag Satpathy %&1130 5 2shish Singh %&1130 ' 2tish +akshi %

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GROUP B 4 SECTION B PGDM (BM) 2013-15

A+,no e./ements

1e wou-d -ike to e3press a who-e%hearted gratitude to a-- those who ha e he-ped with

the report or ha e been associated with the report in any which way and made it a worth%whi-e

e3perience, 1e are great-y indebted to our batch mates and our seniors for ha ing shared their

in a-uab-e e3perience that went a -ong way in the successfu- comp-etion of our report,

2nd* a specia- mention of Prof (Dr) Sambit Mukherjee* who we cannot thank enough

for ha ing gi en us the opportunity and his tota- support for working on such a project and

guiding it to successfu- comp-etion,

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GROUP D 7 SECTION D PGDM (BM) 2013-15

e+#ti e #mmar4

This report is prepared to ana-yse a prob-em and formu-ate its optima- so-ution using the -inear programming method, 2 transportation prob-em for a Bharat Ply, a mid-sized manufacturer ofplywood furniture, has recently merged with K.N. Furniture ompany. Bharat Ply is loo!ing toe"pand its operations. #o do this, it wants to $uild three more factories and reach 2% cities in&ndia. urrently it has only two factories which supply eight cities in &ndia. #he cities it wantsto supply are listed alpha$etically as ' (hmeda$ad, Baroda, Bangalore, handigarh,

hennai, )ehradun, *ydera$ad, &ndore, +aipur, Kanpur, Kol!ata, Kozhi!ode, uc!now,udhiana, um$ai, ysore, New )elhi, Patna, anchi, and /hillong.

Bharat Ply has estimated the costs of transporting finished furniture from its factories to thedifferent cities. &t has also estimated the demand for plywood furniture in each of the twentycities for the coming year. Bharat Ply wants to find out the o0erall least cost of transportationfrom each of the factories to different cities to satisfy o0erall demand. #he cost oftransportation from each of the factories to the cities is gi0en $elow '


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GROUP B 4 SECTION B PGDM (BM) 2013-15

Form# ation of LP Pro$ em

The company '45 produces a product ca--ed +"6P DM#$ which has recent-y gained a good

market share, '45 has setup & factories at different -ocations across pan ndia, To market its product

a-- o er ndia* '45 has identified !" cities across ndia, t has been decided that road wi-- be used for

transportation, The production capacity of the & factories of +"6P DM#$ (in units) is can be -isted

down as7

Fa+tor4 1 5 '0 Fa+tor4 2 51'0 Fa+tor4 3 5'*0 Fa+tor4 * 50 Fa+tor4 5 '3 0

The demand in units of +"6P DM#$ of the !" cities can be jotted down as7

8ity # #!$ 8ity ! !"# 8ity $ #9: 8ity 6 ##;8ity & #:< 8ity 9 #The cost of transportation per unit of B0*PGDM13 by road is as7

8ity # 8ity ! 8ity $ 8ity 6 8ity &=actory # #"9: ;;# #!9" 6:$


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OB6 CT78 7 To reduce the transportation cost of +"6P DM#$ from & different factories to !"

cities across ndia by finding out the minimum distance to be tra e--ed and simu-taneous-y meeting

the demands of the cities according to the supp-y capacities of the factories,

/et ' ij be the units of +"6P DM#$ from =actory i to 8ity j where i > #* !* $* 6* & and j > #* !*,,!" So*

the tota- 8ost of Transportation of the product +"6P DM#$ from the factories to a-- the cities to meet

their demand can be written down as7

#"9: ' ## ? ;;# ' #! ? #!9" ' #$ ? 6:$ ' #6 ?


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(8ost of Transportation from =actory &) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(5)

The sum of the abo e & e.uations gi es the tota- transportation cost of goods from the & factories toa-- the !" cities* which has to be minimi@ed now,

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ConstraintsThe company '45 faces ! types of constraints7

#, The tota- units supp-ied by any factory to a-- the cities put together cannot e3ceed the

tota- production capacity of the factory,

8onstraint for =actory #7

' ##? ' #! ? ' #$ ? ' #6 ? ' #& ? ' #9 ? ' #; ? ' #: ? ' #< 4 ' ##" ? ' ### ? ' ##! ? ' ##$ ? ' ##6 ? ' ##& ?

' ##9 ? ' ##; ? ' ##: ? ' ##< ? ' #!" 56 378%

8onstraint for =actory !7

' !# ? ' !! ? ' !$ ? ' !6 ? ' !& ? ' !9 ? ' !; ? ' !: ? ' !< 4 ' !#" ? ' !## ? ' !#! ? ' !#$ ? ' !#6 ? ' !#& ?

'!#9

? '!#;

? '!#:

? '!# 6#"

8onstraint for 8ity !7

' #! ? ' !! ? ' $! ? ' 6! ? ' &! B> 9;"

8onstraint for 8ity $7

' #$ ? ' !$ ? ' $$ ? ' 6$ ? ' &$ B> &9"

8onstraint for 8ity 67

' #6 ? ' !6 ? ' $6 ? ' 66 ? ' &6 B> &9"

8onstraint for 8ity &7

' #& ? ' !& ? ' $& ? ' 6& ? ' && B> 9$"

8onstraint for 8ity 97

' #9 ? ' !9 ? ' $9 ? ' 69 ? ' &9 B> 9&"

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GROUP D7 SECTION D

PGDM (BM) 2013-15

8onstraint for 8ity ;7

' #; ? ' !; ? ' $; ? ' 6; ? ' &; B> &:"

8onstraint for 8ity :7

' #: ? ' !: ? ' $: ? ' 6: ? ' &: B> #6#"8onstraint for 8ity $;"

8onstraint for 8ity ##7

' ### ? ' !## ? ' $## ? ' 6## ? ' # B> $&"

8onstraint for 8ity #&7

' ##& ? ' !#& ? ' $#& ? ' 6#& ? ' & B> !&"

8onstraint for 8ity #97

' ##9 ? ' !#9 ? ' $#9 ? ' 6#9 ? ' B> #6"

8onstraint for 8ity #;7

' ##; ? ' !#; ? ' $#; ? ' 6#; ? ' B> ;6"

8onstraint for 8ity #:7

' ##: ? ' !#: ? ' $#: ? ' 6#: ? ' : B> 96"

8onstraint for 8ity # 6""

+ecause a-- the ' ijAs are positi e .uantities* we a dd th

' ij C> " for i > #*!*$*6*& and j > #*!*$*6*&*

8ombining the objecti e function* supp-y constraints* demand constraints* and

sign restrictions yie-ds the fo--owing /P formu-ation of '45Asprob-em7

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M 0 5 > #"9: ' ## ? ;;# ' #! ? #!9" ' #$ ? 6:$ ' #6 ?


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:


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Formation of t%e LPP in L7"GOMODEL:! TRANSPORTATION PROBLEM, 5 FACTORIES AND 20 CITIES;

SETS :FACTORY: CAPACITY;CITY: DEMAND;LINKS(FACTORY, CITY): COST, VOLUME;

ENDSETS

! ENTER ALL THE NECESSARY DATA HERE.COST IS IN RS PER UNIT;

DATA :

!ATTRIBUTE VALUES; FACTORY F F2 F" F# F5;

CITY C C2 C" C# C5 C$ C% C& C' C 0 C C 2 C " C # C 5 C $ C % C &C ' C20;

CAPACITY '2 %2 && %'5 $"';

DEMAND 2" 20 $& % &' '5 %# # &% 2&2 2$# 2' 05 %5 #2$$$ '2 5" 20; COST 0$& %% 2$0 #&" '#& 20$ # " '5 #50 "#% "''

"&' 0# # 0 "20&$ 20" %5" 52& &$

"5# #0& %2$ " & & " ' 25 0 $$$ 2 & '$' #%" $"' &&55%0

#%' "'& 50% "#2 0 #2"$ ' "0& "# %'5 '% #$% # 0 "'& #&2 %$5 05$ """5 "&0

'$" &5& 2"' '0' '#&"# "2# #&$ #&" "'& #" %" " ' #"5 2#5 % % %% %'&

#'#02' 2#5 20" ' "&$

"5# "05 #"' 0'5 0$5 $0$ #25 % % 5%" "5$ #'# 0# 5'#%5$ #"% #&5 2'" #" 22 2#5;ENDDATA

! THE OB ECTIVE (MINIMUM) FUNCTION;MIN SUM (LINKS( I, ): COST( I, ) * VOLUME( I, ));

! THE DEMAND SIDE CONSTRAINTS;FOR ( CITY( ): SUM ( FACTORY( I): VOLUME( I, )) DEMAND( ));

! THE SUPPLY SIDE CONSTRAINTS;FOR ( FACTORY( I): SUM ( CITY( ): VOLUME( I, )) + CAPACITY( I));

END


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1hen we e3ecute the abo e in / 0 O using (8tr- ? E)* we get the fo--owing7

The Objecti e function a-ue came out to 210 1090

"B T%e %o e so #tion is in A::en.i -79

1hen we want to find out the number of units supp-ied to each city* we e3ecute using (8tr- ? 1),

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o #tion of t%e LPPGlobal optimal solution found.

Objective value: 210710.0Infeasibilities: 0.000000Total solver iterations: 27

Variable Value Reduced ost

VO!"#$% &1' () 117.00000 0.000000

VO!"#$% &1' *) +7.00000 0.000000

VO!"#$% &1' 11) 2(.00000 0.000000

VO!"#$% &1' 1,) 7,.00000 0.000000

VO!"#$% &1' 1*) 10,.00000 0.000000

VO!"#$% &1' 20) 120.00000 0.000000

VO!"#$% &2' 1) 12-.00000 0.000000

VO!"#$% &2' 7) 1,-.00000 0.000000

VO!"#$% &2' 1+) 1*2.00000 0.000000

VO!"#$% &2' 1*) 1 .00000 0.000000

VO!"#$% &-' ,) 1+*.00000 0.000000

VO!"#$% &-' 7) 7.000000 0.000000

VO!"#$% &-' 12) -0.00000 0.000000

VO!"#$% &-' 1 ) (2.00000 0.000000

VO!"#$% &-' 17) .00000 0.000000

VO!"#$% &(' 2) 201.00000 0.000000

VO!"#$% &(' -) 1 +.00000 0.000000

VO!"#$% &(' +) 1(1.00000 0.000000

VO!"#$% &(' 10) 111.00000 0.000000

VO!"#$% &(' 12) 17(.00000 0.000000

VO!"#$% &,' ) 1*,.00000 0.000000

VO!"#$% &,' 11) 70.00000 0.000000

VO!"#$% &,' 1-) 12*.00000 0.000000

VO!"#$% &,' 1() 10,.00000 0.000000

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!es# t 7nter:retation VO!"#$ %&,' 1() 10,.00000 0.000000

The abo e in the output means that #"& units of the demand for 8#6 from factory =&, Simi-ar-y the

resu-ts for the remaining cities can be interpreted, The tota- cost of transporting +"6P DM#$ from

the & factories to the !" cities in the most optima- way is !s 210 1090 ,

The pie charts be-ow show the break up of the cost per factory in percentage of the tota- cost incurredand the bar diagram shows the actua- cost incurred in the cities,

Transpor a !on Cos P"r #a$ or%

2%;

2%;

18;

Factory1Factory2Factory

27; 17;

Factory

Factory 3

Transpor a !on Cos Born" B% Ea$& C! % %,%%%

2 , 22 23,%%% 22,3 :

21,18

2%,%%% 18,893

13,%%% 1 ,1 % 1 ,:12

11, :%

9,%72 :,:2% 1%,:18 ost

1%,%%% :,31 7,9: 7,2 8 8,%18 8,279

,: : 3,1%93 ,1 :2 , 3% 3,%%% 2,873

%

ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity ity1 2 3 8 7 : 9 1% 11 12 1 1 13 18 17 1: 19 2%

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The bar diagrams be-ow disp-ay the percentage of tota- cost incurred by each city of the tota-

cost, =or e3amp-e* 86 spends !,


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1


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APP "D7;-7- / - 1 34 - -6 3 7 8 679.

O/ < 3= = -6 : 2 0% 0.0I78 3/3-3 3 : 0.000000T - -= > 3 > 3 7 : 2%

M 9 - C- : LP

T - = >3 /- : 00N 7-37 > = >3 /- : 0I7 ? > = >3 /- : 0

T - < 7 > 37 : 2$N.7-37;0> 03725: 0

T - 7 7@ > : "00N 7-37 > 7 7@ > : 0

Variable Value Reduced ostCAPACITY( F ) '2.0000 0.000000CAPACITY( F2) %2.0000 0.000000CAPACITY( F") &&.0000 0.000000CAPACITY( F#) %'5.0000 0.000000CAPACITY( F5) $"'.0000 0.000000DEMAND( C ) 2".00000 0.000000DEMAND( C2) 20 .00000 0.000000DEMAND( C") $&.00000 0.000000DEMAND( C#) %.00000 0.000000DEMAND( C5) &'.00000 0.000000DEMAND( C$) '5.00000 0.000000

DEMAND( C%) %#.00000 0.000000DEMAND( C&) # .00000 0.000000DEMAND( C') &%.00000 0.000000DEMAND( C 0) .00000 0.000000DEMAND( C ) 2&2.00000 0.000000DEMAND( C 2) 2$#.00000 0.000000DEMAND( C ") 2'.00000 0.000000DEMAND( C #) 05.00000 0.000000DEMAND( C 5) %5.00000 0.000000DEMAND( C $) #2.00000 0.000000DEMAND( C %) $$$.00000 0.000000DEMAND( C &) '2.00000 0.000000DEMAND( C ') 5".00000 0.000000

DEMAND( C20) 20.00000 0.000000COST( F , C ) 0$&.0000 0.000000COST( F , C2) %% .0000 0.000000COST( F , C") 2$0.0000 0.000000COST( F , C#) #&".0000 0.000000COST( F , C5) '#&.0000 0.000000COST( F , C$) 20$.0000 0.000000COST( F , C%) # ".0000 0.000000COST( F , C&) '5 .0000 0.000000COST( F , C') #50.0000 0.000000COST( F , C 0) "#%.0000 0.000000COST( F , C ) "''.0000 0.000000COST( F , C 2) "&'.0000 0.000000COST( F , C ") 0# .0000 0.000000COST( F , C #) # 0.0000 0.000000COST( F , C 5) "2 .0000 0.000000

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COST( F , C $) 0&$.0000 0.000000COST( F , C %) 20".0000 0.000000COST( F , C &) %5".0000 0.000000COST( F , C ') 52&.0000 0.000000COST( F , C20) &$ .0000 0.000000COST( F2, C ) "5#.0000 0.000000COST( F2, C2) #0&.0000 0.000000COST( F2, C") %2$.0000 0.000000COST( F2, C#) " &.0000 0.000000COST( F2, C5) & ".0000 0.000000COST( F2, C$) '.0000 0.000000COST( F2, C%) 25.0000 0.000000COST( F2, C&) 0 .0000 0.000000COST( F2, C') $$$.0000 0.000000COST( F2, C 0) 2 &.0000 0.000000COST( F2, C ) '$'.0000 0.000000COST( F2, C 2) #%".0000 0.000000COST( F2, C ") $"'.0000 0.000000COST( F2, C #) &&5.0000 0.000000COST( F2, C 5) 5%0.0000 0.000000COST( F2, C $) #%'.0000 0.000000COST( F2, C %) "'&.0000 0.000000COST( F2, C &) 50%.0000 0.000000COST( F2, C ') "#2.0000 0.000000COST( F2, C20) 0 #.0000 0.000000COST( F", C ) 2"$.0000 0.000000COST( F", C2) '.0000 0.000000COST( F", C") "0&.0000 0.000000COST( F", C#) "# .0000 0.000000COST( F", C5) %'5.0000 0.000000COST( F", C$) '%.0000 0.000000COST( F", C%) #$%.0000 0.000000COST( F", C&) # 0.0000 0.000000COST( F", C') "'&.0000 0.000000COST( F", C 0) #&2.0000 0.000000COST( F", C ) %$5.0000 0.000000COST( F", C 2) 05$.0000 0.000000COST( F", C ") ".0000 0.000000COST( F", C #) ""5.0000 0.000000COST( F", C 5) "&0.0000 0.000000COST( F", C $) '$".0000 0.000000COST( F", C %) &5&.0000 0.000000COST( F", C &) 2"'.0000 0.000000COST( F", C ') '0'.0000 0.000000COST( F", C20) '#.0000 0.000000COST( F#, C ) &"#.0000 0.000000COST( F#, C2) "2#.0000 0.000000COST( F#, C") #&$.0000 0.000000COST( F#, C#) #&".0000 0.000000COST( F#, C5) "'&.0000 0.000000COST( F#, C$) #" .0000 0.000000COST( F#, C%) %".0000 0.000000COST( F#, C&) ".0000 0.000000COST( F#, C') '.0000 0.000000COST( F#, C 0) #"5.0000 0.000000COST( F#, C ) 2#5.0000 0.000000COST( F#, C 2) % %.0000 0.000000COST( F#, C ") %% .0000 0.000000COST( F#, C #) %'&.0000 0.000000COST( F#, C 5) #'#.0000 0.000000

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COST( F#, C $) 02'.0000 0.000000COST( F#, C %) 2#5.0000 0.000000COST( F#, C &) 20".0000 0.000000COST( F#, C ') '.0000 0.000000COST( F#, C20) "&$.0000 0.000000COST( F5, C ) 0$2.0000 0.000000COST( F5, C2) "05.0000 0.000000COST( F5, C") #"'.0000 0.000000COST( F5, C#) 0'5.0000 0.000000COST( F5, C5) 0$5.0000 0.000000COST( F5, C$) $0$.0000 0.000000COST( F5, C%) #25.0000 0.000000COST( F5, C&) % %.0000 0.000000COST( F5, C') 5%".0000 0.000000COST( F5, C 0) "5$.0000 0.000000COST( F5, C ) #'#.0000 0.000000COST( F5, C 2) 0# .0000 0.000000COST( F5, C ") 5'#.0000 0.000000COST( F5, C #) %5$.0000 0.000000COST( F5, C 5) #"%.0000 0.000000COST( F5, C $) #&5.0000 0.000000COST( F5, C %) 2'".0000 0.000000COST( F5, C &) #".0000 0.000000COST( F5, C ') 22.0000 0.000000COST( F5, C20) 2#5.0000 0.000000VOLUME( F , C ) 0.000000 52&.0000VOLUME( F , C2) 0.000000 2$#.00000VOLUME( F , C") 0.000000 '%.0000VOLUME( F , C#) %.00000 0.000000VOLUME( F , C5) 0.000000 0".0000VOLUME( F , C$) 0.000000 2"".0000VOLUME( F , C%) 0.000000 "#.00000VOLUME( F , C&) 0.000000 ".0000VOLUME( F , C') &%.00000 0.000000VOLUME( F , C 0) 0.000000 2#".0000VOLUME( F , C ) 2#.00000 0.000000VOLUME( F , C 2) 0.000000 $".0000VOLUME( F , C ") 0.000000 &2.0000VOLUME( F , C #) 0.000000 %5".0000VOLUME( F , C 5) %5.00000 0.000000VOLUME( F , C $) 0.000000 '".00000VOLUME( F , C %) 0.000000 $%.0000VOLUME( F , C &) 0.000000 20.00000VOLUME( F , C ') 05.00000 0.000000VOLUME( F , C20) 20.00000 0.000000VOLUME( F2, C ) 2".00000 0.000000VOLUME( F2, C2) 0.000000 &%.00000VOLUME( F2, C") 0.000000 & .00000VOLUME( F2, C#) 0.000000 %.000000VOLUME( F2, C5) 0.000000 20.0000VOLUME( F2, C$) 0.000000 52&.0000VOLUME( F2, C%) 5".00000 0.000000VOLUME( F2, C&) 0.000000 2 0.0000VOLUME( F2, C') 0.000000 "#.0000VOLUME( F2, C 0) 0.000000 2$2.0000VOLUME( F2, C ) 0.000000 %5$.0000VOLUME( F2, C 2) 0.000000 25".0000VOLUME( F2, C ") 0.000000 0.0000VOLUME( F2, C #) 0.000000 "&.0000VOLUME( F2, C 5) 0.000000 #"5.0000

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VOLUME( F2, C $) 0.000000 &5&.0000VOLUME( F2, C %) 0.000000 2'#.0000VOLUME( F2, C &) '2.00000 0.000000VOLUME( F2, C ') $.00000 0.000000VOLUME( F2, C20) 0.000000 ".0000VOLUME( F", C ) 0.000000 &0.0000VOLUME( F", C2) 0.000000 "2 .0000VOLUME( F", C") 0.000000 #&".0000VOLUME( F", C#) 0.000000 2"#.0000VOLUME( F", C5) &'.00000 0.000000VOLUME( F", C$) 0.000000 %&.0000VOLUME( F", C%) %.000000 0.000000VOLUME( F", C&) 0.000000 22'.0000VOLUME( F", C') 0.000000 2$#.0000VOLUME( F", C 0) 0.000000 2"$.0000VOLUME( F", C ) 0.000000 %0.00000VOLUME( F", C 2) "0.00000 0.000000VOLUME( F", C ") 0.000000 '2.00000VOLUME( F", C #) 0.000000 %#.0000VOLUME( F", C 5) 0.000000 "0 .0000VOLUME( F", C $) #2.00000 0.000000VOLUME( F", C %) $$$.00000 0.000000VOLUME( F", C &) 0.000000 "0.0000VOLUME( F", C ') 0.000000 %5.00000VOLUME( F", C20) 0.000000 5'.00000VOLUME( F#, C ) 0.000000 5'.0000VOLUME( F#, C2) 20 .00000 0.000000VOLUME( F#, C") $&.00000 0.000000VOLUME( F#, C#) 0.000000 $ .00000VOLUME( F#, C5) 0.000000 " #.0000VOLUME( F#, C$) 0.000000 "$'.0000VOLUME( F#, C%) 0.000000 5.00000VOLUME( F#, C&) # .00000 0.000000VOLUME( F#, C') 0.000000 % %.0000VOLUME( F#, C 0) .00000 0.000000VOLUME( F#, C ) 0.000000 02'.0000VOLUME( F#, C 2) %#.00000 0.000000VOLUME( F#, C ") 0.000000 5".0000VOLUME( F#, C #) 0.000000 "2#.0000VOLUME( F#, C 5) 0.000000 "5$.0000VOLUME( F#, C $) 0.000000 "5.0000VOLUME( F#, C %) 0.000000 %2$.0000VOLUME( F#, C &) 0.000000 2" .0000VOLUME( F#, C ') 0.000000 25&.0000VOLUME( F#, C20) 0.000000 2"$.0000VOLUME( F5, C ) 0.000000 # .0000VOLUME( F5, C2) 0.000000 2"".0000VOLUME( F5, C") 0.000000 &".0000VOLUME( F5, C#) 0.000000 % .0000VOLUME( F5, C5) 0.000000 0'.0000VOLUME( F5, C$) '5.00000 0.000000VOLUME( F5, C%) 0.000000 5.000000VOLUME( F5, C&) 0.000000 %.00000VOLUME( F5, C') 0.000000 &.000000VOLUME( F5, C 0) 0.000000 2 ".0000VOLUME( F5, C ) %0.00000 0.000000VOLUME( F5, C 2) 0.000000 #2.00000VOLUME( F5, C ") 2'.00000 0.000000VOLUME( F5, C #) 05.00000 0.000000VOLUME( F5, C 5) 0.000000 ""'.0000

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GROUP D 7 SECTION DPGDM (BM) 2013-15

VOLUME( F5, C $) 0.000000 '".0000VOLUME( F5, C %) 0.000000 $#.0000VOLUME( F5, C &) 0.000000 %.0000VOLUME( F5, C ') 0.000000 $5.0000VOLUME( F5, C20) 0.000000 '5.00000

Ro/ lac or urplus ual 3rice2 0% 0.0 .000000

2 0.000000 2"2.0000" 0.000000 22 .0000# 0.000000 2%5.00005 0.000000 2 ".0000$ 0.000000 %'5.0000% 0.000000 22 .0000& 0.000000 #$%.0000' 0.000000 2# .0000

0 0.000000 $0$.00000.000000 25&.0000

2 0.000000 &5.0000" 0.000000 05$.0000# 0.000000 2 %.00005 0.000000 & ".0000$ 0.000000 5'.0000% 0.000000 '$".0000& 0.000000 &5&.0000' 0.000000 '.0000

20 0.000000 22&.00002 0.000000 ""'.000022 0.000000 52.000002" 0.000000 "#2.00002# 0.000000 0.000000

25 0.000000 ".00002$ 0.000000 '.00000

b4 or assignment ashish

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