Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?
A)(0, 0)
B)(0, 100)
C)(65, 65)
D)(100, 0)

Question

Quizplus · Accepted Answer

Every point that satisfies all the constraints is a feasible solution. The optimal solution is the feasible solution that maximizes (or minimizes) the objective function. In this case, since there is no objective function given, we cannot determine the optimal solution. However, we can determine which points are feasible solutions.

We can graph the constraints and find the feasible region:

The feasible region is the shaded region. We can see that all four points are in the feasible region. However, point C is located on the boundary of the feasible region, which means that it is a corner point. In linear programming, the optimal solution is always a corner point of the feasible region. Therefore, point C could potentially be the optimal solution, and it cannot be eliminated as a possible choice.

Points A, B, and D are not corner points, so they are less likely to be optimal solutions. However, they are still feasible solutions, and one of them could potentially be the optimal solution.

Consider the Following Constraints from a Linear Programming Problem: 2X