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In case of solution of a two variable linear programming problems by graphical method, one constraint line comes parallel to the objective function line. Then the problem will have
- a)infeasible solution
- b)unbounded solution
- c)degenerate solution
- d)infinite number of optimal solutions
Correct answer is option 'D'. Can you explain this answer?
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In case of solution of a two variable linear programming problems by g...
Solution:
When solving a two-variable linear programming problem by graphical method, if one of the constraint lines is parallel to the objective function line, then the problem will have an infinite number of optimal solutions.
Explanation:
To understand why this is the case, let's consider the following example of a two-variable linear programming problem:
Maximize Z = 3x + 2y
Subject to:
2x + y ≤ 10
3x + y ≥ 12
x, y ≥ 0
We can graph the two constraint lines and the objective function line on the same coordinate plane as shown below:
As we can see, the constraint line 3x + y = 12 is parallel to the objective function line Z = 3x + 2y. This means that any point on the constraint line will have the same objective function value of Z = 12.
Since the feasible region of the problem is bounded (i.e., it is a polygon), there must be at least one corner point that is optimal. However, any corner point that lies on the constraint line 3x + y = 12 will be optimal since it has the same objective function value as any other point on that line.
Therefore, the problem has an infinite number of optimal solutions, all of which lie on the constraint line 3x + y = 12.
Conclusion:
When one of the constraint lines is parallel to the objective function line in a two-variable linear programming problem solved by graphical method, the problem will have an infinite number of optimal solutions.
When solving a two-variable linear programming problem by graphical method, if one of the constraint lines is parallel to the objective function line, then the problem will have an infinite number of optimal solutions.
Explanation:
To understand why this is the case, let's consider the following example of a two-variable linear programming problem:
Maximize Z = 3x + 2y
Subject to:
2x + y ≤ 10
3x + y ≥ 12
x, y ≥ 0
We can graph the two constraint lines and the objective function line on the same coordinate plane as shown below:
As we can see, the constraint line 3x + y = 12 is parallel to the objective function line Z = 3x + 2y. This means that any point on the constraint line will have the same objective function value of Z = 12.
Since the feasible region of the problem is bounded (i.e., it is a polygon), there must be at least one corner point that is optimal. However, any corner point that lies on the constraint line 3x + y = 12 will be optimal since it has the same objective function value as any other point on that line.
Therefore, the problem has an infinite number of optimal solutions, all of which lie on the constraint line 3x + y = 12.
Conclusion:
When one of the constraint lines is parallel to the objective function line in a two-variable linear programming problem solved by graphical method, the problem will have an infinite number of optimal solutions.
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In case of solution of a two variable linear programming problems by graphical method, one constraint line comes parallel to the objective function line. Then the problem will havea)infeasible solutionb)unbounded solutionc)degenerate solutiond)infinite number of optimal solutionsCorrect answer is option 'D'. Can you explain this answer?
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