Merton Truck case study
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8/20/2019 Merton Truck case study
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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
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*u!, e!t product mi- ould "e /
%odel 101 = 2000
%odel 102 = 1000
1.(b)
X Y 1))) 1001
Per_Unit_proft 3000 5000
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 ,+++
Per_Unit_proft 3000 5000
Fixed_overhead86000
00
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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
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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 @/&
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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
Per_Unit_proft 3000 5000
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+