Linear Programming Problems and Solutions | Desklib

1) a)
Dual of the problem is
Minimize v=6 y1 +7 y2+ 10 y3
Subject to:
12 y1−3 y2 ≥ 2
y1 + y2 + y3 ≥ 1
y3 ≥0
y1 ≥0 , y2 ≥0
b) Solution of Primal
The leaving variable is P1 and entering variable is P2.

The optimal solution value is Z = 6
X1 = 0
X2 = 6
The optimal solution value is Z = 7
X1 = 0
X2 = 7
Shadow prices of constraint 1
= (7-6)/ (1) = 1
The optimal solution value is Z = 6
X1 = 0
X2 = 6
Shadow prices of constraint 2
= (6-6)/ (1) = 0
The optimal solution value is Z = 6
X1 = 0
X2 = 6
Shadow prices of constraint 3
= (6-6)/ (1) = 0
Solution of dual

The optimal solution value is Z = 6
X1 = 1
X2 = 0
X3 = 0
Solution of the dual matches with the shadow prices of the primal. So shadow prices solve
the dual problem.
2)