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Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?
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Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: O...
Solution to linear programming problem
Objective function:
Z = 4x1 + 6x2
Constraints:
x1 + x2 ≤ 4
3x1 + x2 ≤ 12
x1, x2 ≥ 0
Step 1: Plotting the constraints
To solve the linear programming problem graphically, we need to plot the constraint lines on the coordinate plane.
x1 + x2 ≤ 4 can be rewritten as x2 ≤ -x1 + 4, which gives us the line:
x2 = -x1 + 4
Similarly, 3x1 + x2 ≤ 12 can be rewritten as x2 ≤ -3x1 + 12, which gives us the line:
x2 = -3x1 + 12
Plotting these two lines on the coordinate plane, we get the following graph:
The feasible region is the shaded area that satisfies all the constraints.
Step 2: Finding the corner points
To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region. The corner points are the vertices of the feasible region.
In this case, the corner points are:
(0, 0), (0, 4), (2, 2), and (4, 0)
Step 3: Evaluating the objective function
We evaluate the objective function Z = 4x1 + 6x2 at each corner point:
Z(0, 0) = 0
Z(0, 4) = 24
Z(2, 2) = 20
Z(4, 0) = 16
Step 4: Conclusion
The optimal solution is Z = 24 at (0, 4).
Answer: The solution to the linear programming problem is unique.
Objective function:
Z = 4x1 + 6x2
Constraints:
x1 + x2 ≤ 4
3x1 + x2 ≤ 12
x1, x2 ≥ 0
Step 1: Plotting the constraints
To solve the linear programming problem graphically, we need to plot the constraint lines on the coordinate plane.
x1 + x2 ≤ 4 can be rewritten as x2 ≤ -x1 + 4, which gives us the line:
x2 = -x1 + 4
Similarly, 3x1 + x2 ≤ 12 can be rewritten as x2 ≤ -3x1 + 12, which gives us the line:
x2 = -3x1 + 12
Plotting these two lines on the coordinate plane, we get the following graph:
The feasible region is the shaded area that satisfies all the constraints.
Step 2: Finding the corner points
To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region. The corner points are the vertices of the feasible region.
In this case, the corner points are:
(0, 0), (0, 4), (2, 2), and (4, 0)
Step 3: Evaluating the objective function
We evaluate the objective function Z = 4x1 + 6x2 at each corner point:
Z(0, 0) = 0
Z(0, 4) = 24
Z(2, 2) = 20
Z(4, 0) = 16
Step 4: Conclusion
The optimal solution is Z = 24 at (0, 4).
Answer: The solution to the linear programming problem is unique.
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Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?
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Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? 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 to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?.
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? 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 to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?.
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