An integer programming (maximization)problem was first solved as a linear programming problem, and the objective function value (profit)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 = 12 Y = 32
B)X = 12 Y = 33
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) will change the solution. Given that this is a maximization problem and the original solution likely utilized the fractional parts of X and Y to reach the maximum, any adjustment to integers will likely result in a lower maximum, hence the objective function value must be less than $253.67.

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