Numerical Methods and Optimization

Duality and Sensitivity Analysis in Linear Programming 301

zx

B

x

N

rhs

10−(c

T

N

− c

T

B

B

−1

N) c

T

B

B

−1

b

0 I

m

B

−1

NB

−1

b

(12.19)

More specifically, we will use the formulas in (12.19) to answer the following

important questions:

(1) Will the current basis still remain feasible after a given change in the

problem input data?

(2) Will the current basis still remain optimal after a given change in the

problem input data?

(3) How can we find a new optimal solution if the feasibility or optimality

of the optimal basis for the original LP is altered by the change in the

input data?

The first question can be addressed by checking whether the vector of the

right-hand sides of the ...