linear programming production strategy bodyplus 100,200

7/26/2019 Linear programming Production strategy bodyplus 100,200

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Graphical Method

Presented By

Prabhat Taneja 221090

Preeti Sharma 221096

Rajdeep Baruah - 221113


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INDEX

CASE STUDY : Production StrategyBETTER FITNESS INC. (BFI)

Page number 85-86

Using graphical method

FORE School of Management


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BFI wants to manufacture its twomachines :

BodyPlus 100

BodyPlus 200



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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



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BodyPlus 100 And BodyPlus 200There 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.



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BodyPlus 100Machine

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



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BodyPlus 200Machineand

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



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Machine and

Welding Time

Painting and

finishing time

Assembling,

Testing and

Packaging Time

Labor Cost Perhour $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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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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Authorized dealers can purchase at 70% of thesuggested price :

BodyPlus 100s price =0.70 x 2400 = $1680

BodyPlus 200sprice = 0.70 x 3500 = $2450

This is the price at which it is sold to Dealers.

President stated that the number of units of theBodyPlus 200 produced must be at least 25 percent of

the total production.

Calculating Retail Cost



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BP100 :

Total cost= raw material cost + labour cost

=1050 + 259= $1309

Price sold= $1680

Profit = 16801309 = $371

BP200 :

Total cost = raw material cost + labour cost

1575 + 414= $1989

Price sold = $2450

Profit = 24501989 = $461

Calculating Profit



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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=0



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Plotted using MATLAB

8X1+ 12X2


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Max Z = 371X1+461X2

Optimal solution: X1 = 50, X2 = 50/3 or 16.667, Profit = $26,233.487.

1

.

. Boundary points0,0

0,4530,30

50,16.66

.


.


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2 Case without constraint of producing at least 25% ofBP200 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


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Max Z = 371X1+461X2

Optimal solution: X1 = 60, X2 = 10 Profit= $ 26870.000FORE School of Management

..

.

..

Boundary

points

0,00,45

30,30

60,10

70,0


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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


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Where should efforts be expended in order toincrease profits?

Arriving at the optimal solution considering the constraint ofproducing at least 25% BP200 of the total production, we cansee that machine and welding time is fully utilized.

3


8*50 + 12*16.66= 600

5*50 + 10*16.667


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BIBLIOGRAPHY and REFERENCE

An Introduction to Management Science

Quantitative Approaches to Decision Making

MATLABPreparation of Line Graph

Wolframalpha.comPreparation of Inequality

Graph


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THANK YOU

linear programming production strategy bodyplus 100,200

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