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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution?
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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x1...
Solution of Lp Problem
Problem Statement:
Maximize z = 2x1 + 4x2, subject to:
x1 + 2x2 ≤ 5
x1x2 ≤ 4
x1, x2 ≥ 0
Solution:
1. Feasible Region:
The feasible region is the set of all points that satisfy the constraints of the problem. The feasible region for this problem is given by the shaded area in the figure below.
2. Corner Points:
The corner points of the feasible region are the points where the constraints intersect. The corner points for this problem are (0, 0), (0, 2), (2, 1), and (5/2, 0).
3. Objective Function:
To find the maximum value of the objective function, we evaluate it at each corner point.
At (0, 0), z = 2(0) + 4(0) = 0
At (0, 2), z = 2(0) + 4(2) = 8
At (2, 1), z = 2(2) + 4(1) = 10
At (5/2, 0), z = 2(5/2) + 4(0) = 5
Therefore, the maximum value of the objective function is 10, which occurs at the point (2, 1).
4. Answer:
The LP problem has an alternative optima, which means there are multiple optimal solutions with the same maximum value of the objective function. In this case, the corner point (0, 2) is also an optimal solution with a maximum value of 8.
Hence, the answer is (A) Has alternative optima.
Problem Statement:
Maximize z = 2x1 + 4x2, subject to:
x1 + 2x2 ≤ 5
x1x2 ≤ 4
x1, x2 ≥ 0
Solution:
1. Feasible Region:
The feasible region is the set of all points that satisfy the constraints of the problem. The feasible region for this problem is given by the shaded area in the figure below.
2. Corner Points:
The corner points of the feasible region are the points where the constraints intersect. The corner points for this problem are (0, 0), (0, 2), (2, 1), and (5/2, 0).
3. Objective Function:
To find the maximum value of the objective function, we evaluate it at each corner point.
At (0, 0), z = 2(0) + 4(0) = 0
At (0, 2), z = 2(0) + 4(2) = 8
At (2, 1), z = 2(2) + 4(1) = 10
At (5/2, 0), z = 2(5/2) + 4(0) = 5
Therefore, the maximum value of the objective function is 10, which occurs at the point (2, 1).
4. Answer:
The LP problem has an alternative optima, which means there are multiple optimal solutions with the same maximum value of the objective function. In this case, the corner point (0, 2) is also an optimal solution with a maximum value of 8.
Hence, the answer is (A) Has alternative optima.
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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution?
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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution?.
Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x2≤4,x18x220 Ops: A. B. Has alternative optima Has degeneracy value C. Has unbounded solution D. Has infeasible solution?.
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