1. Graphical Method
Presented By
Prabhat Taneja – 221090
Preeti Sharma – 221096
Rajdeep Baruah - 221113

2. INDEX
CASE STUDY : Production Strategy
BETTER FITNESS INC. (BFI)
Page number 85-86
Using graphical method
FORE School of Management

3. BFI wants to manufacture its two
machines :
 BodyPlus 100
 BodyPlus 200
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4. BodyPlus 100 consists of :
a) Frame Unit
b) Press Station
c) Pec -Dec Station
BodyPlus 200 consists of :
a) Frame Unit
b) Press Station
c) Pec -Dec Station
d) Leg Press station
FORE School of Management

5. BodyPlus 100 And BodyPlus 200
There are various activities involved in per unit
manufacturing of body plus 100 and body plus 200 :
 Machining and welding
 Painting and finishing
 Assembling, packaging and testing
These activities take different amount of time.
FORE School of Management

6. BodyPlus 100
Machine
and welding
time(in
hours)
Painting and
finishing
time(in hours)
Assembling,
Testing and
packaging
time(in hours)
Raw
Material
Cost ($)
Packa
ging
Cost
($)
Frame Unit 4 2
2
450
50
Press Station 2 1 300
Pec-Dec Station 2 2 250
Total 8 5 2 1000
FORE School of Management

7. BodyPlus 200
Machine
and
welding
time(in
hours)
Painting and
finishing
time(in hours)
Assembling,
Testing and
packaging
time(in hours)
Cost
($)
Packagi
ng Cost
($)
Frame Unit 5 4
2
650
75
Press Station
3 2 400
Pec-Dec Station 2 2
250
Leg-Press Station 2 2 200
Total 12 10 2 1500
FORE School of Management

8. Machine and
Welding Time
Painting and
finishing time
Assembling,
Testing and
Packaging Time
Labor Cost Per
hour $20 $15 $12
Total Time(hrs) Cost per hour ($)
Machine and Welding
Time
600 20
Painting and finishing
time
450 15
Assembling, Testing
and Packaging Time
140 12
For the next production period management estimates the hours and labour cost :
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9. Retail Price of BodyPlus 100 = $2400
Retail Price of BodyPlus 200 = $3500
Labour cost for BodyPlus 100= (20x8)+(15x5)+(12x2)= $259
Labour cost BodyPlus 200 = (20x12)+(15x10)+(12x2)= $414.
Raw material cost for BodyPlus 100 = $1000 +$50 = $1050
(with $50 as assembling ,packaging and testing cost.)
Raw material cost for BodyPlus 200 = $1500 + $75 = $1575
(with $75 as assembling ,packaging and testing cost.)
Calculating Manufacturing Cost
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10. Authorized dealers can purchase at 70% of the
suggested price :
BodyPlus 100‘s price =0.70 x 2400 = $1680
BodyPlus 200’s price = 0.70 x 3500 = $2450
This is the price at which it is sold to Dealers.
President stated that the number of units of the
BodyPlus 200 produced must be at least 25 percent of
the total production.
Calculating Retail Cost
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11. BP100 :
Total cost= raw material cost + labour cost
=1050 + 259= $1309
Price sold= $1680
Profit = 1680 – 1309 = $371
BP200 :
Total cost = raw material cost + labour cost
1575 + 414= $1989
Price sold = $2450
Profit = 2450 – 1989 = $461
Calculating Profit
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12. A)Decision Variable involved are :
X1 = Number of units of BodyPlus 100 to be produced.
X2 = Number of units of BodyPlus 200 to be produced.
B)LPP Equation (Profit Maximization Equation) :
Max Z = 371X1 +461X2
C)Constraints :
1) Machine and Welding Hours :
8X1 + 12X2<= 600
2) Painting and Finishing Hours :
5X1 + 10X2 <= 450
3) Assembly and Packaging Hours :
2X1 + 2X2 <= 140
4) X2 >= 0.25(X1 +X2)
5) Non Negative Constraints :
X1 >=0 , X2 >=0
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13. Plotted using MATLAB
8X1 + 12X2<= 600; 5X1 + 10X2 <= 450; 2X1 + 2X2 <= 140; X2 >= 0.25(X1 +X2)
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14. Max Z = 371X1 +461X2
Optimal solution: X1 = 50, X2 = 50/3 or 16.667, Profit = $26,233.487.
1
.
. Boundary points
0,0
0,45
30,30
50,16.66
.
FORE School of Management
.

15. FORE School of Management
2 Case without constraint of producing at least 25% of
BP200 out of the total production
Using the following 4 constraints we can plot the required
region to check the optimal solution for case 2.
8X1 + 12X2<= 600
5X1 + 10X2 <= 450
2X1 + 2X2 <= 140
X1 >=0 , X2 >=0

16. Max Z = 371X1 +461X2
Optimal solution: X1 = 60, X2 = 10 Profit= $ 26870.000
FORE School of Management
.
.
.
..
Boundary
points
0,0
0,45
30,30
60,10
70,0

17. FORE School of Management
Effect of producing BP100 and BP200 without the constraint
of number of BP200 to be at least 25% of the TOTAL production
Profit margin increases by -> $26870 - $26233.487
$636.513

18. Where should efforts be expended in order to
increase profits?
Arriving at the optimal solution considering the constraint of
producing at least 25% BP200 of the total production, we can
see that machine and welding time is fully utilized.
3
FORE School of Management
8*50 + 12*16.66= 600
5*50 + 10*16.667 <= 450 ------ SLACK of 33.33 hours
2*50 + 2*16.667 <= 140 ------ SLACK of 6.68 hours
While there is a slack in the painting and finishing time and
Assembly time. Thus by increasing the Machine and Welding
time , we can successfully increase profits by utilizing the
slack in painting and assembling time.

19. FORE School of Management
BIBLIOGRAPHY and REFERENCE
•An Introduction to Management Science –
Quantitative Approaches to Decision Making
•MATLAB – Preparation of Line Graph
•Wolframalpha.com – Preparation of Inequality
Graph

20. FORE School of Management
THANK YOU