Vuhelper
01-07-2012, 04:51 PM
1): Use Two-phase Simplex Method to solve the following Linear Programming Problem;
Minimize Z = x1 – 2×2 – 3×3
Subject to constraints;
–2×1+x2+3×3 = 2
2×1+3×2+4×3 =1
x1,x2≥0
2): Discuss whether the degeneracy of the following Linear Programming Problem occurs at initial or subsequent snow stage of its solution. Give the complete description along with its solution.
Maximize Z= 3x+9y
Subject to;
x + 4y≤8
x + 2y≤4
x,y≥0
3): Discuss why the Duality Principle is of advantageous in case of solving the following Linear Programming Problem;
Minimize Z = x + y + u + v + t + r
Subject to
x+r≥7
x+y≥20
y+u≥14
u+v≥20
t+r≥10
with x,y,u,v,t,r≥0
Minimize Z = x1 – 2×2 – 3×3
Subject to constraints;
–2×1+x2+3×3 = 2
2×1+3×2+4×3 =1
x1,x2≥0
2): Discuss whether the degeneracy of the following Linear Programming Problem occurs at initial or subsequent snow stage of its solution. Give the complete description along with its solution.
Maximize Z= 3x+9y
Subject to;
x + 4y≤8
x + 2y≤4
x,y≥0
3): Discuss why the Duality Principle is of advantageous in case of solving the following Linear Programming Problem;
Minimize Z = x + y + u + v + t + r
Subject to
x+r≥7
x+y≥20
y+u≥14
u+v≥20
t+r≥10
with x,y,u,v,t,r≥0