An integer programming (minimization)problem was first solved as a linear programming problem, and the objective function value (cost)was $253.67.The two decision variables (X, Y)in the problem had values of X = 12.45 and Y = 32.75.If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem?
A)X = 13 Y = 33
B)X = 12 Y = 32
C)The objective function value must be less than $253.67.
D)The objective function value will be greater than $253.67.

Question

Quizplus · Accepted Answer

Since the original solution to the linear programming problem was not in integers, rounding to the nearest integers (either up or down) to meet the integer constraint will necessarily change the objective function value. Given that this is a minimization problem, and the original solution likely represents the minimum possible value without the integer constraints, any adjustment to meet the integer constraints will result in a solution that is less optimal (i.e., has a higher cost) than the original. Therefore, the objective function value in the optimal integer solution will be greater than $253.67.

An Integer Programming (Minimization)problem Was First Solved as a Linear