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The Linear Programming Problem Has an Unusual Characteristic

Question 21

Multiple Choice

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 + 2y

Constraints:

X ≥ 0
Y ≥ 0
X ≤ 10
X + y ≤ 8


A) ​ 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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​ A) ​   The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16 B)    The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8 C)    The constraint x ≤ 10 is extraneous.No minimum. D)    The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8 E)    The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0 The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16
B) 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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​ A) ​   The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16 B)    The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8 C)    The constraint x ≤ 10 is extraneous.No minimum. D)    The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8 E)    The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0 The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8
C) 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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​ A) ​   The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16 B)    The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8 C)    The constraint x ≤ 10 is extraneous.No minimum. D)    The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8 E)    The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0 The constraint x ≤ 10 is extraneous.No minimum.
D) 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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​ A) ​   The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16 B)    The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8 C)    The constraint x ≤ 10 is extraneous.No minimum. D)    The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8 E)    The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0 The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8
E) 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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​ A) ​   The constraint x ≤ 10 is extraneous.Minimum at (0,8) : 16 B)    The constraint x ≤ 10 is extraneous.Minimum at (8,0) : -8 C)    The constraint x ≤ 10 is extraneous.No minimum. D)    The constraint x ≤ 10 is extraneous.Minimum at (8,8) : 8 E)    The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0 The constraint x ≤ 10 is extraneous.Minimum at (0,0) : 0

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