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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x1...
Solution of Lp Problem
Given Lp problem:
max z=2x1+4x2
subject to: x1+2x2≤5,
x1+x2≤4,
x1≥0,x2≥0
To solve the given Lp problem, we will use the Simplex method.
Step 1: Convert the given Lp problem into standard form
max z=2x1+4x2
subject to: x1+2x2+x3=5,
x1+x2+x4=4,
x1≥0,x2≥0,x3≥0,x4≥0
Step 2: Write the initial Simplex tableau
CB | x3 x4 | RHS
----------------------
z | -2 -4 | 0
x3 | 1 0 | 5
x4 | 0 1 | 4
Step 3: Select the entering variable
Since the objective function z has negative coefficient for both x1 and x2, we can choose either x1 or x2 as the entering variable. Let's choose x1.
Step 4: Select the leaving variable
To select the leaving variable, we need to find the minimum ratio of RHS to the coefficient of the entering variable in each constraint. For x1, the ratios are:
5/1 = 5
4/1 = 4
Since the minimum ratio is 4, x4 will be the leaving variable.
Step 5: Perform row operations to update the tableau
We will use row operations to make the pivot element (1,1) equal to 1 and to make all other elements in the column equal to 0.
CB | x3 x1 | RHS
----------------------
z | 0 -2 | -8
x3 | 1 1/2 | 5/2
x4 | 0 1 | 4
Step 6: Repeat steps 3 to 5 until the optimal solution is reached
We can repeat steps 3 to 5 to find the optimal solution. The optimal solution is:
z = 14/3
x1 = 2/3
x2 = 8/3
Answer: A. Has alternative optima.
Given Lp problem:
max z=2x1+4x2
subject to: x1+2x2≤5,
x1+x2≤4,
x1≥0,x2≥0
To solve the given Lp problem, we will use the Simplex method.
Step 1: Convert the given Lp problem into standard form
max z=2x1+4x2
subject to: x1+2x2+x3=5,
x1+x2+x4=4,
x1≥0,x2≥0,x3≥0,x4≥0
Step 2: Write the initial Simplex tableau
CB | x3 x4 | RHS
----------------------
z | -2 -4 | 0
x3 | 1 0 | 5
x4 | 0 1 | 4
Step 3: Select the entering variable
Since the objective function z has negative coefficient for both x1 and x2, we can choose either x1 or x2 as the entering variable. Let's choose x1.
Step 4: Select the leaving variable
To select the leaving variable, we need to find the minimum ratio of RHS to the coefficient of the entering variable in each constraint. For x1, the ratios are:
5/1 = 5
4/1 = 4
Since the minimum ratio is 4, x4 will be the leaving variable.
Step 5: Perform row operations to update the tableau
We will use row operations to make the pivot element (1,1) equal to 1 and to make all other elements in the column equal to 0.
CB | x3 x1 | RHS
----------------------
z | 0 -2 | -8
x3 | 1 1/2 | 5/2
x4 | 0 1 | 4
Step 6: Repeat steps 3 to 5 until the optimal solution is reached
We can repeat steps 3 to 5 to find the optimal solution. The optimal solution is:
z = 14/3
x1 = 2/3
x2 = 8/3
Answer: A. Has alternative optima.
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Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O Has unbounded solution D. Has infeasible solution?.
Solution of Lp Problem, max z=2x1 4x2,subject to: x1 2x2≤5, x1 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O 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 x254,x18x220 Ops: A. Has alternative optima B. Has degeneracy value C. O Has unbounded solution D. Has infeasible solution?.
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