Dakota example revisited.

$-$ What are the optimal dual variable values?

$-$ How do we change the optimal table given above if a new variable y$4>=0$ is added to the dual problem with objective function coefficient $15$ and column vector of constraint coefficients $(1,0,2)$T$?$

$-$ How do we change the optimal table given above if a new variable y$4<=0$ is added to the dual problem with objective function coefficient $15$ and column vector of constraint coefficients $(2,1,0)$T$?$