merton truck case study

8/20/2019 Merton Truck case study

http://slidepdf.com/reader/full/merton-truck-case-study 1/6

Let,

X= No. of model 101 produced

Y= No. of model 102 produced

The linear formation will beObjective :

Max 3000 X + 5000 Y

Subjected to:

1X+ 2Y ≤ 4000, Engine !!em"l#

2X + 2Y ≤ $000, %etl !tmping

2X ≤ 5000, %odel 101 !!em"l#

3Y ≤ 4500, %odel 102 !!em"l#

X &= 0, non negti'it#

Y &= 0, non negti'it#

1. ()

X Y Total_proft

2000 1000 2400000

Per_Unit_proft 3000 5000

Fixed_Overhead 8600000

Engine_asse!l" 1 2 4000 #$ 4000

%etal_&taping 2 2 6000 #$ 6000%odel_101_assse!l" 2 0 4000 #$ 5000%odel_102_'sse!l" 0 3 3000 #$ 4500

%odel_101 1 0 2000 ($ 0

%odel102 0 1 1000 ($ 0



*u!, e!t product mi- ould "e /

%odel 101 = 2000

%odel 102 = 1000

1.(b)

X Y 1))) 1001


Fixed_Overhead86000

00

Engine_asse!l" 1 2 4001

%etal_&taping 2 2 6000%odel_101_assse!l" 2 0 3))8%odel_102_'sse

!l" 0 3 3003%odel_101 1 0 1)))

%odel102 0 1 1001

e!t product mi- en cpcit# ere ri!ed incre!ed i!/ Model 101 = 1999

Model 102 = 1001

*onstraints

Fina

lShadow

Constraint

Allowable

Allowable

Cell NameValu

e PriceR!Side

"ncrease

#ecrease

+,+13 %odel 101 ./&

2000 0 0 2000 1E30

+,+14 %odel 102 ./&

1000 0 0 1000 1E30

$#$%

&n'ineassembl( )!S

*+++ ,+++ 4000 500 500

+,+10

%etal &taping./&

6000 500 6000 500 1000

+,+1

1

%101 'sse!l"

./&

400

0 0 5000 1E30 1000+,+12

%102 'sse!l"./&

3000 0 4500 1E30 1500

E-tr unit of cpcit# i! ort 2000

-.c/ X Y Totalproft

Extra_nit_orth

1)00 1100260000

0 ,+++


Fixed_overhead86000

00



Engine_asse!l" 1 2 4100 #$ 4100

%etal_&taping 2 2 6000 #$ 6000%odel_101_assse!l" 2 0 3800 #$ 5000

%odel_102_'sse!l" 0 3 3300 #$ 4500

%odel_101 1 0 1)00 ($ 0

%odel102 0 1 1100 ($ 0ontri"ution in prt " = 2000

ontri"ution en cpcit# i! incre!ed from 4001 to 4100 = 200000

*erefore ontri"ution in profit i! incre!ing t rte of 2000 per unit mcine our of engine

!!em"l#.

1.(d)

Fina

l ShadowConstra

intAllowa

bleAllowa

ble

Cell NameValue Price

R!Side

"ncrease

#ecrease

+,+1

3 %odel 101 ./&

150

0 0 0 1500 1E30+,+14 %odel 102 ./&

1500 0 0 1500 1E30

$#$%

&n'ineassembl( )!S

*0++ + *1++ -&23+ -++

+,+10

%etal &taping./&

6000 1500 6000 200 3000

+,+11

%101 'sse!l"./&

3000 0 5000 1E30 2000

+,+12

%102 'sse!l"./&

4500

666666666 4500 300 3000

500 unit! of engine cpcit# cn "e dded "efore it cpcit# ort cnge!.

do price "ecome! 0.

2. Prodtion anager is taling a!ot rei!rsing the otside spplier

7or aterials la!or and overhead 9t Fixed overheads are !ased on



Engine_asse!l" 1 2 08 4000 #$ 4000

%etal_&taping 2 2 15 6000 #$ 6000%odel_101_assse!l" 2 0 1 4000 #$ 5000

%odel_102_'sse!l" 0 3 0 3000 #$ 4500

%odel101 1 0 0 2000 ($ 0

%odel102 0 1 0 1000 ($ 0

%odel103 0 0 1 0 ($ 0

() No %erton !ould not produce 103 truc< "ecu!e it! contri"ution to profit i! not

enoug.

(") *e ort of contri"ution of 103 truc< model for profit !ould "e t le!t

2000+350=2350

Final

Reduced

Objective

Allowable

Allowable

Cell Name

Value Cost

Coe5cient

"ncrease

#ecrease

+9+2 ;

2000 0 3000 2000 500

+*+2 =

1000 0 5000 1000 2000

+,+2 > 0 0 2000 30+ 1E30

>.4 *e ompn# !ould not go for o'ertime "ecu!e it! profit decre!e! from 2400000 to

2350000.

X1= No of 101 truc< produced in o'er time

Y1=No of 102 truc< produce in o'er time

X Y X- Y- Proft

?o_o7_Units 1000 1500 500 023500

00

*ontri!tion 3000 5000 2400 3800

Fixed_Overhead)3500

00

./& @elati @/&



on

Engine_asse!l" 1 2 0 0 4000 #$ 4000

Over_tie_or 0 0 1 2 500 #$ 2000

%etal_&taping 2 2 2 2 6000 #$ 6000%odel_101_assse

!l" 2 0 2 0 3000 #$ 5000%odel_102_'sse!l" 0 3 0 3 4500 #$ 4500

%odel_101 1 0 0 0 1000 ($ 0

%odel102 0 1 0 0 1500 ($ 0

Extra_101 0 0 1 0 500 ($ 0

Extra_102 0 0 0 1 0 ($ 0

.&

*e num"er of 101 model truc< i! ! time% of 102 model truc<, o '=!

'! = 0, ic i! dditionl con!trint.

X Y Total_pro

ft

,,0+ 60+ 1)00000


Fixed_Overhead86000

00

Engine_asse!l" 1 2 350 #$ 4000

%etal_&taping 2 2 6000 #$ 6000%odel_101_assse!l" 2 0 4500 #$ 5000

@elation 1 A3 0 $ 0%odel_102_'sse!l" 0 3 2250 #$ 4500

%odel_101 1 0 2250 ($ 0

%odel102 0 1 50 ($ 0

The prodt ix ill !e

?o o7 101 Tr 78,,0+9?o o7 102 Tr9 (860+

merton truck case study

Documents