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 feasible solution to the integer linear programming problem.
A) always
B) sometimes
C) optimally
D) never

Question

Quizplus · Accepted Answer

In this type of linear programming problem, all feasible solutions have integer values for decision variables. Therefore, rounding down the optimal solution values will result in a feasible solution to the integer linear programming problem. Moreover, since the objective function coefficients are all positive, rounding down will not increase the objective function value, so the feasible solution will also be optimal.

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