How can the following Linear Program be characterized?
Min X + Y
Subject to
X ≤ 20
Y ≤ 5
X + Y ≥ 40
X, Y ≥ 0
A) bounded and feasible
B) unbounded and feasible
C) bounded and infeasible
D) unbounded and infeasible
E) this is not a Linear Program

Question

Quizplus · Accepted Answer

The feasible region of this linear program is a triangle with vertices at (0, 5), (20, 20), and (40, 0). Since the objective function is to minimize X + Y, the optimal solution occurs at one of these vertices. However, none of the vertices satisfy the constraint X + Y ≥ 40, which means that the linear program is infeasible. Therefore, the correct choice is (C) bounded and infeasible.

How Can the Following Linear Program Be Characterized