Suppose you want to minimize an objective function z=2x₁+3x₂. Both decision variables must be integer. The optimal solution to the LP relaxation will: A) be smaller than the optimal IP solution B) be larger than the optimal IP solution C) can be either smaller or larger than the optimal IP solution D) will be within 5% of the optimal IP solution value

Question

Quizplus · Accepted Answer

The optimal solution to the LP relaxation (allowing for fractional values of the decision variables) will always be smaller than or equal to the optimal solution of the Integer Programming (IP) problem, because the LP relaxation is a relaxation of the IP problem, removing the integrality constraints and thus enlarging the feasible region.

Suppose You Want to Minimize an Objective Function Z=2x1+3x2

Suppose You Want to Minimize an Objective Function Z=2x₁+3x₂