Читать книгу Optimizations and Programming - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 33

Consider the LP

The dual of this program is:

The solution of the primal is x* = (1, 0, 1)T .

The optimal dual solution can be constructed from additional slack conditions:

 – the condition = 0 is satisfied because x* is admissible;

 – the condition (cj − pT Aj)xj = 0 is satisfied for j = 2:- for j = 1, this condition becomes:5p1 + 3p2 = 13.- for j = 3, it becomes:3p1 = 6.

These two conditions give p₁ = 2 and p₂ = 1. This solution is dual admissible. The total dual cost is 19, and so is the primal cost.