Problem $\mathrm{A}$ is a two-variable linear programming problem with a maximization objective function. Problem B is a two-variable pure integer programming problem obtained from Problem A by requiring the variables to be integers and leaving all other things unchanged. Assuming that both problems have optimal solutions, the objective function value of problem A will always be the objective function value of Problem B.
A) greater than
B) less than
C) equal to
D) greater than or equal to
E) less than or equal to

Question

Quizplus · Accepted Answer

In linear programming problems, allowing variables to take any real values (including fractions) can lead to an optimal solution that is not possible when variables are restricted to integer values, as in integer programming problems. Therefore, the optimal solution of a linear programming problem (Problem A) can be equal to or better (higher in the case of maximization) than that of the corresponding integer programming problem (Problem B) because the latter has more restrictive conditions.

Problem A\mathrm{A}A Is a Two-Variable Linear Programming Problem with a Maximization Objective

Problem $\mathrm{A}$ Is a Two-Variable Linear Programming Problem with a Maximization Objective