Choose the most correct of the following statements relating to p… - Vidyadip

Question

Choose the most correct of the following statements relating to primal - dual linear programming problems:

Shadow prices of resources in the primal are optimal values of the dual variables.
The optimal values of the objective functions of primal and dual are the same.
If the primal problem has unbounded solution, the dual problem would have infeasibility.
All of the above.

✓

Answer

All of the above.

Solution:

From the primal - dual relationship, The shadow prices of resources in the primal are optimal values of the dual variables.

If one of the problems has an optimal feasible solution then the other problem also has an optimal feasible solution.

The optimal objective function value is same for both primal and dual problems.

If one problem has an unbounded solution then the other problem is infeasible.

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