engineering management

1. Engineering Management 19/12/2013
LP: Simplex
Method Solution
MD MOUDUD HASAN
LECTURER, AIE, HSTU
19/12/2013 1
• 1)Two foods A and B contain calcium, protein and Calories. Each Kg of
food A contains 10 units of calcium, 5 units of protein and 2 units of
calories. Each kg of food B contains 4 units of calcium, 5 units of protein
and 6 units of calories. The minimum daily requirement of calcium,
protein and calories are 20 units, 20 units and 12 units respectively. The
cost of food A is Tk. 60/kg and B is Tk. 100/kg. Determine the optimum
amount of each food combination, which will satisfy the specified
nutritional requirements and minimize the total cost of the diet.
• Solution:
• Let, X1= amount of food A to be consumed per day, kg
X2= amount of food B to be consumed per day, kg
Objective function,
Minimum cost C= 60X1+100 X2
Subject to,
10X1+4X2 ≥20
5X1+5X2 ≥20
2X1+6X2 ≥12
X1,X2 ≥0
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M M Hasan, Lecturer, AIE, HSTU, Dinajpur. 1

2. Engineering Management 19/12/2013
• 2)The management of Padma Oil Company has received orders from
Bangladesh Railway to supply 600 units of diesel and 500 units gasoline.
Padma oil company has two processes that can be used ( Process A and
process B) for manufacturing of diesel and gasoline. One hour of process
A produces 5 units of diesel and 10 units of gasoline. One hour of process
B produces 8 units of diesel and 6 units of gasoline. Process A uses a
particular combination of crude’s which cost Tk. 7 per hour, Process B
uses different combination of crude’s which cost Tk. 9.20 per hour. Find
the optimal mix of process A and process B.
• Solution:
• Let, X1= No. of hours process A to be run
X2= No. of hours process B to be run
Objective function,
Minimum cost C= 7X1+9.2X2
Subject to,
5X1+8X2 =600
10X1+6X2=500
X1,X2 ≥0 19/12/2013 3
3)
Objective function,
Maximize profit, Z= 4X1+3X2+7X3
Subject to,
2X1+X2 +3X3≤120
X1+3X2+2X3=120
X1,X2,X3 ≥0
Find the optimum value of X1,X2 and X3 for maximization of
profit Z?
Solution:
Z- 4X1-3X2-7X3- 0X4+MX5=0
Subject to,
2X1+X2 +3X3+X4 =120
X1+3X2+2X3 +X5 =120
X1,X2,X3 ≥0 X5 = 0
………………………….(1)
………………………….(2)
………………………….(3)
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M M Hasan, Lecturer, AIE, HSTU, Dinajpur. 2

3. Engineering Management 19/12/2013
EN BV Z X1 X2 X3 X4 X5 R.H.S Ratio
1 unadjusted 1 -4 -3 -7 0 M 0
2 0 2 1 3 1 0 120
3 0 1 3 2 0 1 120
EN BV Z X1 X2 X3 X4 X5 R.H.S Ratio
1 Z 1 -4-M -3-3M -7-2M 0 0 -120M -
2 X4 0 2 1 3 1 0 120 120
3 X5 0 1 3 2 0 1 120 40
EN BV Z X1 X2 X3 X4 X5 R.H.S Ratio
1 Z 1 -3 0 -5 0 1+M 120 -
2 X4 0 5/3 0 7/3 1 -1/3 80 240/7
3 X2 0 1/3 1 2/3 0 1/3 40 60
EN BV Z X1 X2 X3 X4 X5 R.H.S Ratio
1 Z 1 4/7 0 0 15/7 2/7+M 2040/7
2 X3 0 5/7 0 1 3/7 -1/7 240/7
3 X2 0 -2/3 1 0 -2/7 3/7 120/7 19/12/2013 5
Solution
• There are no negative values in step 4 so this is the
optimum solution,
Z=2040/7
X1=0
X2=120/7
X3=240/7
X4=0
X5=0
19/12/2013 6
M M Hasan, Lecturer, AIE, HSTU, Dinajpur. 3

4. Engineering Management 19/12/2013
Assignment-2
• A farm grows soybeans and corns on its 500 acres 0f
land. An acre of soybeans brings a TK. 100 profit and
an acre of corn brings a Tk. 200 profit. Because of
government regulations, no more than 200 acres can
be planted in soybeans. During the planting season
1200 man-hours of planting time will be available.
Each acre of soybeans requires 2 man-hours, while
each acre of corn requires 6 man-hours. How many
acres of soybean and how many acres of corn
should be planted in order to maximize profits.
Both in graphical and simplex method.
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M M Hasan, Lecturer, AIE, HSTU, Dinajpur. 4