How can the following Linear Program be characterized?
Min X + 2Y
Subject to
X ≤ 20
Y ≤ 5
X, Y ≥ -40
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 is a rectangle with vertices (-40,-40), (-40,5), (20,-40), and (20,5). Since the objective function is a linear function, it attains its minimum value at one of the vertices of the feasible region. Therefore, the optimal solution must occur at one of the vertices of the feasible region. Since the feasible region is bounded and there are only a finite number of vertices, the problem is both bounded and feasible.

How Can the Following Linear Program Be Characterized