If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem.
A) always, optimal
B) always, non-optimal
C) never, non-optimal
D) sometimes, optimal

Question

Quizplus · Accepted Answer

Rounding down the optimal solution values of the decision variables in a maximization problem with the given constraints and coefficients might sometimes result in an optimal solution for the integer linear programming problem, but not always. This is because the integer solution could still be feasible and potentially optimal, depending on the specific structure of the problem and the distance of the LP solution from the nearest integers.

If a Maximization Linear Programming Problem Consists of All Less-Than-Or-Equal-To