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Consider the following LPP
Minimize z = 5x1 + 7x2 + x3
s/t: 2x1 − x2 + 4x3 ≤ 10
x1 , x2 , x3 ≥ 0
The solution for the above LPP is
- a)unbounded
- b)unique
- c)no solution
- d)infinitely many
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + ...
Standard form:
z − 5x1 − 7x2 − x3 = 0
2x1 − x2 + 4x3 + s1 = 10
Most Upvoted Answer
Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + ...
Explanation:
- Unbounded Solution:
The given Linear Programming Problem (LPP) is unbounded because the objective function z = 5x1 + 7x2 + x3 can be increased indefinitely without violating any of the constraints.
- Feasible Region:
The constraint 2x1 - x2 + 4x3 ≤ 10 defines a feasible region in the x1-x2-x3 space. The feasible region is unbounded, which means there are no restrictions on how far x1, x2, and x3 can go.
- Objective Function:
Since the coefficients of x1, x2, and x3 in the objective function are all positive, increasing any of these variables will increase the objective function value. As there are no restrictions on how large x1, x2, and x3 can be, the objective function z can be increased indefinitely.
- Conclusion:
Therefore, the solution for the given LPP is unbounded, as there are no limitations on how much the objective function can be improved. This implies that the optimal solution is not finite and can be increased infinitely.
- Unbounded Solution:
The given Linear Programming Problem (LPP) is unbounded because the objective function z = 5x1 + 7x2 + x3 can be increased indefinitely without violating any of the constraints.
- Feasible Region:
The constraint 2x1 - x2 + 4x3 ≤ 10 defines a feasible region in the x1-x2-x3 space. The feasible region is unbounded, which means there are no restrictions on how far x1, x2, and x3 can go.
- Objective Function:
Since the coefficients of x1, x2, and x3 in the objective function are all positive, increasing any of these variables will increase the objective function value. As there are no restrictions on how large x1, x2, and x3 can be, the objective function z can be increased indefinitely.
- Conclusion:
Therefore, the solution for the given LPP is unbounded, as there are no limitations on how much the objective function can be improved. This implies that the optimal solution is not finite and can be increased infinitely.
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Community Answer
Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + ...
Standard form:
z − 5x1 − 7x2 − x3 = 0
2x1 − x2 + 4x3 + s1 = 10
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Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer?.
Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following LPPMinimize z = 5x1 + 7x2 + x3s/t: 2x1 − x2 + 4x3 ≤ 10x1 , x2 , x3 ≥ 0The solution for the above LPP isa) unboundedb) uniquec) no solutiond) infinitely manyCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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