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.
Z = x + y

Constraints:

X ≥ 0
Y ≥ 0
X + y ≤ 1
3x + y ≤ 6

A) The constraint 3x + y ≤ 6 is extraneous.Minimum at (1,1): 9
B) The constraint 3x + y ≤ 6 is extraneous.No minimum.
C) The constraint 3x + y ≤ 6 is extraneous.Minimum at (1,0): 4
D) The constraint 3x + y ≤ 6 is extraneous.Minimum at (0,0): 0
E) The constraint 3x + y ≤ 6 is extraneous.Minimum at (0,1): 5

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. ​
Z = x + y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y ≤ 1
3x + y ≤ 6
​
A)​ The constraint 3x + y ≤ 6 is extraneous.Minimum at (1,1): 9 
B)​ The constraint 3x + y ≤ 6 is extraneous.No minimum. 
C)​ The constraint 3x + y ≤ 6 is extraneous.Minimum at (1,0): 4 
D) The constraint 3x + y ≤ 6 is extraneous.Minimum at (0,0): 0 
E)​ The constraint 3x + y ≤ 6 is extraneous.Minimum at (0,1): 5

Quizplus · Accepted Answer

The unusual characteristic of this linear programming problem is that the solution region is unbounded. This can be seen in the graph of the solution region, where the feasible region extends infinitely in the positive x and y directions. The minimum value of the objective function is 0, which occurs at the origin (0,0) since this is the only point in the feasible region that satisfies the condition Z = x + y.

The Linear Programming Problem Has an Unusual Characteristic