OR-ASSIGNMENT 2
To be submitted on April 15 2009
1) Find the primal to dual relationship and write the dual for the following LPP. Solve
the dual and read the solution of the primal from the solution of the dual.
Min w = 0.12x1 + 0.15x2
STC 60x1 + 60x2 >=300
12x1 + 6x2 >=36
10x1 +30x2>=90
x1, x2>=0
ANS:Z=33/50
2) Use Dual Simplex method to solve Max Z= -2x1 -x3,
STC x1+x2-x3>=5
x1- 2x2 + 4x3 >=8
x1 x2 x3 >=0
Also write the dual ie min Z and find the value of y1 and y2 from the solution
obtained in dual simplex solved above.
ANS: Z= -9
3) Use Dual Simplex method to solve Min Z=6x1 +7x2 + 3x3 + 5x4
STC 5x1 + 6x2 -3x3 + 4x4 >=12
X2 + 5x3- 6x4 >=10
2x1+ 5x2+ x3+ x4 >=8
X1x2x3x4>=0
ANS: Z= 258/11
4) Solve using Revised Simplex method
a) Max Z=x1+x2+3x3
STC 3x1+2x2+x3 <=3
2x1+x2+2x3<=2
X1x2x3>=0
ANS: Z=3
b) Max Z=3x1+2x2+5x3
STC x1+2x2+x3<=430
3x1+2x3<=460
X1+4x2<=420
X1x2x3>=0
ANS: Z=1350
5) Solve using Two Phase method
a) Max Z =3x1-x2
STC 2x1+ x2 >=2
X1+3x2<=2
X2<=4
X1 x2>=0
ANS: Z= 6
b) Min Z = 15/2 x1 - 3x2
STC 3x1- x2- x3 >=3
X1- x2+ x3 >=2
X1x2x3>=0
ANS: Z=75/8
6) Solve using Big –M method
a) Min Z=2x1 + 9x2 + x3
STC x1+ 4x2+ 2x3 >=5
3x1+ x2+ 2x3 >=4
X1x2x3>=0
ANS:Z = 5/2
b) Max R=5x1- 2x2- x3
STC 2x1+ 2x2- x3>=2
3x1-4x2 >=3
X2+ 3x3 >=5
X1x2x3>=0
ANS: R = 5
7) Explain the Two Phase method for solving a LPP.
8) What are the advantages of Revised Simplex method over Simplex method .
9) Explain Primal-Dual relationship.
10) Explain how do you solve a LPP using Revised Simplex method.