Let us change the sense of the inequality in problem (2.48):

Clearly, the problem is unbounded. Applying the rules of Table 2.4, swapping the columns corresponding to primal and dual problems, we immediately find its dual:

which is clearly infeasible, since the first two conditions on the dual variable are not compatible with the third one.

As a further check, we may work with the equivalent standard form of problem (2.52), 

whose dual is 

with dual variable \(q\). The variable substitution \(=q\) yields the same infeasible dual as above.

Data From Problem 2.48

Data From Problem 2.52

Data From Table 2.4

Transcribed Image Text:

max 1 + 2x2 s.t. x1+x24 x1, x2 0.