Page 97 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes

Task Find the dual to following problem:

Maximise Z = 4x + 5x + 3x + 6x
1 2 3 4
Subject to x + 3x + x + 2x  2
1 2 3 4
3x + 3x + 2x + 2x  4
1 2 3 4
3x + 2x + 4x 5x  6
1 2 3 4
x , x , x , x  0
1 2 3 4
4.3 Advantages of Duality

1. It is advantageous to solve the dual of a primal having less number of constraints because
the number of constraints usually equals the number of iterations required to solve the
problem.
2. It avoids the necessity for adding surplus or artificial variables and solves the problem
quickly (the technique is known as the primal-dual method).
3. The dual variables provide an important economic interpretation of the final solution of
an LP problem.

4. It is quite useful when investigating changes in the parameters of an LPP (the technique
known as sensitivity analysis).
5. Duality is used to solve an LPP by the simplex method in which the initial solution is
infeasible.

Did u know? The dual of the dual problem is again the primal problem.

Task Find out the managerial significance of Duality with the help of some real life
cases.

Self Assessment

State true or false:
1. One part of a Linear Programming Problem (LPP) is called the Primal and the other part is
called the Dual.
2. In the primal problem, the objective function is a exponential combination of n variables.
3. In the dual problem, the dual vector multiplies the constants that determine the positions
of the constraints in the primal.
4. Duality is quite useful when investigating changes in the parameters of an LPP( the
technique known as sensitivity analysis).
5. It is advantageous to solve the dual of a primal having less number of constraints because
the number of constraints usually equals the number of iterations required to solve the
problem.

92 LOVELY PROFESSIONAL UNIVERSITY