Suppose you want to maximize 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 Linear Programming (LP) relaxation of an Integer Programming (IP) problem is generally larger than or equal to the optimal solution of the IP problem itself when maximizing, because the LP relaxation allows for fractional values of the decision variables, potentially accessing feasible solutions not available in the integer-constrained version.

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

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