Solver Excercise

8/19/2019 Solver Excercise

1/22

Problem Statement

Solution

Formulation Solver Formulation

Objective Function 18

Maximize Proft 8

Constraints Objective Function =

Raw Material Constraint

Labor Hours Constraint Raw Material sa!e =

"on#ne!ativit$ Constraint Labor Hour sa!e =

% frm &ro'uces two &ro'ucts( % an' )* +ac, unit o- % re.uires / 0! o- raw material an' lw,ereas eac, unit o- &ro'uct ) re.uires 2 0! o- raw material an' 2 ,ours o- labor* +ver$ w34 0! o- raw material an' 53 labor ,ours* One unit o- &ro'uct % an' ) !ive &roft o- Rs* 4

Formulate t,is &roblem as a linear &ro!rammin! &roblem to 'etermine as to ,ow man$ unibe &ro'uce' &er wee0 so t,at t,e frm can earn t,e maximum &roft*

x1 =

7 = 4x1 26x

/x

/ =

/x1 2x

/ 9 34

x1 2x

/ 9 53

x1( x

/ : 4


2/22

1444

34

53

bor ,ours -or &rocessin!(e0( t,e frm ,as an availabilit$ o-n' Rs* 26 res&ectivel$*

s o- eac, o- t,e &ro'ucts s,oul'


3/22

Problem Statement

Solution

Formulation Solver Formulation

Objective Function

Minimize Proft

&,os&,ate usa!e =Constraints nouro!en usa!e=

P,os&,ate Re.uirement

"itro!en Re.uirement

"on#ne!ativit$ Constraint

;,e a!ricultural researc, institute su!!este' a -armer to s&rea' out at least 844 0! o- a s


4/22

x1= 4

x/= 1

z= 263


5/22

Costs

Supply

3 8 8 40

3 8 3 < 60

6 < 3 8 40

Demand 20 30 40 50

%llocations

Supply

/4 /4 1*


6/22

Solution

Objective Function

Minimize Cost = 834


7/22

Costs

Supply

2 / 1 35

6 3 2 55

< 8 2 60

< 5 2 20Demand 50 5 35

Supply

4 26 4 26

/< /8 4 66

12 // /6 34

14 4 14 /4

Demand 64 86 26


8/22

Objective Function

Minmize Cost= 816


9/22

Costs Solution

Supply Objective

3 1 50 Minimize C

2 8 < 40

/ 50

Demand 20 !5 35

%llocations

Supply

4 16 26 50

/4 /4 4 40

4 64*444441 4 50

Demand 20 5 35 "40


10/22

Function

st = 616


11/22

Costs

Supply

3 1 50 Minimize Cost=

2 8 < 40

/ 60

Demand 20 #5 35

Supply

4 16 26 50

/4 4 4 20

4 34 4 60

Demand 20 #5 35


12/22

256


13/22

Pro$ts

Supply

1/ 18 3 /6 60

8 < 14 18 30

1 2 11 /4 40

Demand 20 30 60 20

%llocations

Supply

14 24 4 /4 60

4 4 24 4 30

14 4 24 4 40

Demand 20 30 60 20 "30


14/22

Solution

Objective Function

Maximize Proft = 1524


15/22

Pro$ts

Supply

/4 1 13 500

5 < 16 400

Demand 200 300 600


16/22

Pro$ts

Supply

6


17/22

Problem Statement

Solution

;,e owner o- a rea'$#ma'e !arments store sells two t$&es o- &remium s,irts( 0nown as 7eea &roft o- Rs /44 an' Rs 244 &er s,irt on 7ee an' ?tar s,irts( res&ectivel$* He ,as two tailorstitc, t,e s,irts* ;ailor % can 'evote a total o- 1< ,ours &er 'a$( w,ile tailor 8 can !ive at t,

o- s,irts are stitc,e' b$ bot, t,e tailors* ;,e time nee'e' -or stitc,in! a 7ee s,irt is / ,ours)* ?imilarl$( a ?tar s,irt re.uires ,ours b$ tailor % an' 2 ,ours b$ tailor )* How man$ s,irtin or'er to maximise 'ail$ &roft@ Formulate it as an inte!er &ro!rammin! &roblem*


18/22

#s,irts an' ?tar#s,irts* He ma0es( % an' )* at ,is 'is&osal tomost 16 ,ours a 'a$* )ot, t$&e

b$ tailor % an' 2 ,ours b$ tailoro- eac, t$&e s,oul' be stitc,e'


19/22

Problem Statement

AtemB % ) C >ei!,t DtonnesEB 2 6 3

Per unit alueB /4 /6 2/ //

Solution

Solver Formulation

x1 x/ x2 x

4 1 1 1

>ei!,t= 16

alue= ,ic, items( an' w,at .uantities s,oul' be loa'e't,e value o- t,e car!o trans&orte'@


20/22

6 tonnes* ;,e wei!,ts an'on t,e &lane so as to maximise


21/22

Problem Statement

Anvestment "et Present alue D"PE Cas, OutGow

A /4(444 1/(444

AA /8(444 1(444

AAA 18(644


22/22

s, outGow re.uire' -or eac, o-' t,at x444 ;,e com&an$estment AA i- it invests in

est in investmenton as maximisation o- "P*

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