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The solution for the LPP is
Max z = 3x1 + 2x2
s/t: 2x1 + 3x2 ≤ 30
3x1 + 2x2 ≤ 24
x1 + x2 ≥ 3
x1 , x2 ≥ 0
- a)Unique optimal
- b)Alternate optimal
- c)Degenerate
- d)Unbounded
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + ...
Given,
2x1 + 3x2 ≤ 30 (0,10)(15, 0)
3x1 + 2x2 ≤ 24 (0, 12)(8, 0)
x1 + x2 ≥ 3 (0, 3)(3, 0)
z = 3x1 + 2x2
z(3,0) = 9
z(0,3) = 6
z(0,10) = 20
z(2.4,8.4) = 24
z(8,0) = 24
Most Upvoted Answer
The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + ...
Given,
2x1 + 3x2 ≤ 30 (0,10)(15, 0)
3x1 + 2x2 ≤ 24 (0, 12)(8, 0)
x1 + x2 ≥ 3 (0, 3)(3, 0)
z = 3x1 + 2x2
z(3,0) = 9
z(0,3) = 6
z(0,10) = 20
z(2.4,8.4) = 24
z(8,0) = 24
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Community Answer
The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + ...
Explanation:
Feasible Region:
The given constraints form a feasible region in the x1-x2 plane. The feasible region is the region bounded by the lines 2x1 + 3x2 = 30, 3x1 + 2x2 = 24, x1 + x2 = 3 and the axes.
Optimality:
1. The objective function z = 3x1 + 2x2 represents a linear function that increases in the direction of the objective vector (3, 2).
2. By analyzing the slopes of the objective function and the constraints, we can see that the objective vector (3, 2) is parallel to the constraint 3x1 + 2x2 = 24.
3. This indicates that there are multiple optimal solutions along this constraint line, making it an alternate optimal solution.
Alternate Optimal Solution:
Since the objective vector is parallel to the constraint 3x1 + 2x2 = 24, there are multiple points on this line that can be optimal solutions. This means that there are alternate optimal solutions that can maximize the objective function z = 3x1 + 2x2.
Therefore, the correct answer is option 'B' - Alternate optimal.
Feasible Region:
The given constraints form a feasible region in the x1-x2 plane. The feasible region is the region bounded by the lines 2x1 + 3x2 = 30, 3x1 + 2x2 = 24, x1 + x2 = 3 and the axes.
Optimality:
1. The objective function z = 3x1 + 2x2 represents a linear function that increases in the direction of the objective vector (3, 2).
2. By analyzing the slopes of the objective function and the constraints, we can see that the objective vector (3, 2) is parallel to the constraint 3x1 + 2x2 = 24.
3. This indicates that there are multiple optimal solutions along this constraint line, making it an alternate optimal solution.
Alternate Optimal Solution:
Since the objective vector is parallel to the constraint 3x1 + 2x2 = 24, there are multiple points on this line that can be optimal solutions. This means that there are alternate optimal solutions that can maximize the objective function z = 3x1 + 2x2.
Therefore, the correct answer is option 'B' - Alternate optimal.
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The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. 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 The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. 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 The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. Can you explain this answer?.
The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. 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 The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. 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 The solution for the LPP isMax z = 3x1 + 2x2s/t: 2x1 + 3x2 ≤ 303x1 + 2x2 ≤ 24x1 + x2 ≥ 3x1 , x2 ≥ 0a) Unique optimalb) Alternate optimalc) Degenerated) UnboundedCorrect answer is option 'B'. Can you explain this answer?.
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