Question

If you add a constraint to an optimization model, and the previously optimal solution satisfies the new constraint, will this solution still be optimal with the new constraint added? Why or why not?

Answer 1

ANSWER:

Consider the use of solver for an optimization problem. Assuming linear behavior , a feasible region and an optimal solution is obtained.

Now add another constraint to the model, If the previous solution satisfies new constraint it will remain as an optimal solution. If previous solution is not within new feasible region then another solution will be there whose value will be lower than the previous solution.

We illustrate this graphically. Consider a LP Model with feasible region as shown.

From the graph above, an optimal solution at the point (1,6) is observed. Other points do not give optimal solution.

Now an extra Constraint as added. As shown in the graph below, a new corner point is added. This new point is not optimal solution as observed clearly from the graph. The graph obtained after adding a new constraint is given below.

This if a new constraint is satisfied by the previously obtained optimal solution, the solution still remains optimal with the new constraint added.