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 unusual characteristic of this problem is that the feasible region is unbounded. This can be seen in the graph, where the feasible region extends infinitely in two directions. Since the objective function is linear and the feasible region is unbounded, there is no minimum value for the objective function. However, the objective function can be minimized to 0 by setting both x and y to 0, which occurs at point (0, 0).

The Linear Programming Problem Has an Unusual Characteristic