Wednesday, 14 March 2012


Assignment III
Linear Programming Problems
Simplex Method

Q1.    Maximize (Z) = 3x1+5x2+4x3       
Subject to constraints   
2x1+3x2≤8
0x1+2x2+5x3≤10
3x1+2x2+4x3≤15
Non Negative Restrictions x1, x2, x3≥0
Ans:Z=765/41 X1=89/41, X2=50/41, X3=62/41

Q2     Maximize (Z) = 4x1+3x2   
Subject to constraints   
2x1+x2≤1000
x1+x2≤800
x1≤400,
x2≤700,
Non Negative Restrictions x1, x2, ≥0
Ans:  Z=2600, X1=200, X2=600

Q3     Maximize (Z) = 10x1+20x2            
Subject to constraints   
5x1+3x2≤30
3x1+6x2≤36,
2x1+5x2≤20,
Non Negative Restrictions x1, x2, ≥0
Ans:  Z=120, X1=4.8, X2=3.6

Q4.    Maximize (Z) = 10x1+15x2+20x3             
Subject to constraints   
10x1+5x2+2x3≤2700,
5x1+10x2+4x3≤2200,
x1+x2+2x3≤500
Non Negative Restrictions x1, x2, x3≥0
Ans:  Z=174.4 X1=0, X2=150, X3=174.4

Q5     Maximize (Z) = 6x1+8x2   
Subject to constraints   
30x1+20x2≤300
5x1+10x2≤110,
Non Negative Restrictions x1, x2, ≥0
Ans:  Z=96, X1=4, X2=9


Q6.    Maximize (Z) = 500x1+600x2+1200x3
Subject to constraints   
2x1+4x2+6x3≤160
3x1+2x2+4x3≤120
Non Negative Restrictions x1, x2, x3≥0
Ans:  Z=32800 X1=8, X2=0, X3=24

Q7.    Maximize (Z) = 5x1+10x2+8x3    
Subject to constraints   
3x1+5x2+2x3≤60
4x1+4x2+4x3≤72
2x1+4x2+5x3≤100
Non Negative Restrictions x1, x2, x3≥0
Ans:  Z=160  X1=0, X2=8, X3=10

Q8.    Maximize (Z) = 30x1+40x2+20x3             
Subject to constraints   
10x1+12x2+7x3≤10,000
7x1+10x2+8x3≤8,000
x1+x2+x3≤1,000
Non Negative Restrictions x1, x2, x3≥0
Ans:  Z=32500  X1=250, X2=625, X3=0

Q9.    Maximize (Z) = 4x1+3x2+5x3-150           
Subject to constraints   
2x1+3x2+2x3≤400
3x1+2x2+2x3≤350
x1+4x2+2x3≤300
Non Negative Restrictions x1, x2, x3≥0
Ans:  Z=637.5  X1=25 X2=0, X3=137.5





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