The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the minimum value of the objective function (if possible)and where it occurs.
Objective function:

Z = x + y

Constraints:

X ≥ 0
Y ≥ 0
-x + y ≤ 1
-x + 5y ≤ 7

A) Minimum at (0,1): 1
B) Minimum at (1.5,0.5): 2
C) Minimum at (0.5,1.5): 2
D) Minimum at (0,0): 0
E) No minimum.

Question

The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the minimum value of the objective function (if possible)and where it occurs. ​
Objective function:
​
Z = x + y
​
Constraints:
​
X ≥ 0
Y ≥ 0
-x + y ≤ 1
-x + 5y ≤ 7
​
A) Minimum at (0,1): 1 
B) Minimum at (1.5,0.5): 2 
C) Minimum at (0.5,1.5): 2 
D)​ Minimum at (0,0): 0 
E) No minimum.

Quizplus · Accepted Answer

The solution region is a triangle bounded by the x-axis, y-axis, and the lines -x+y=1 and -x+5y=7. The unusual characteristic is that the solution region has a vertex at the origin (0,0). The objective function Z = x + y is a linear function with a minimum value at one of the vertices of the solution region. Since the solution region is bounded and non-empty, the minimum value of Z exists. It occurs at the vertex (0,0) and has a value of 0. Therefore, the answer is D.

The Linear Programming Problem Has an Unusual Characteristic