Consider the following LP. subject to: Maximize Z = 60x₁ + 30x₂ + 20x3 8x1 + 6x2 + x3 ≤ 48 4x1 + 2x2 + 3/2 X3 ≤ 20 2x1 + 3/2 x₂ + 1/2 X3 ≤ 8 X1, X2, X3 20 1) Write the associated dual problem.
Consider the following LP. subject to: Maximize Z = 60x₁ + 30x₂ + 20x3 8x1 + 6x2 + x3 ≤ 48 4x1 + 2x2 + 3/2 X3 ≤ 20 2x1 + 3/2 x₂ + 1/2 X3 ≤ 8 X1, X2, X3 20 1) Write the associated dual problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Question #1
Consider the following LP.
Maximize Z = 60x1 + 30x2 + 20x3
subject to:
8x1 + 6x2 + X3 5 48
4x1 + 2x2 + 3/2 x3 < 20
2x1 + 3/2 x2 + 1/2 x3 < 8
X1, X2, X3 2 0
1) Write the associated dual problem.
2) Assume the optimal solution for the primal problem is Z= 280 and the basic variable values are
Sı=24, X3=8 and x1=2. Also, the optimal dual solution is y1=0, y2=10, and y3=10. Answer the
following questions:
30
[43]
6.
to
2
a) Suppose we changed the elements of the column x2 from
dose the optimal
[2/3]
solution remains optimal? justify your answer
[15]
b) Suppose we add new activity x4 to the problem, and we add of the x4 column
1
to the
1
1
problem, dose the current basis remains optimal? justify your answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F713a5577-8533-4f80-b043-7a196f079df2%2Fde3f2b38-b6d1-4bbd-b50e-5aaf4fa697fe%2Ff1z3c2c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question #1
Consider the following LP.
Maximize Z = 60x1 + 30x2 + 20x3
subject to:
8x1 + 6x2 + X3 5 48
4x1 + 2x2 + 3/2 x3 < 20
2x1 + 3/2 x2 + 1/2 x3 < 8
X1, X2, X3 2 0
1) Write the associated dual problem.
2) Assume the optimal solution for the primal problem is Z= 280 and the basic variable values are
Sı=24, X3=8 and x1=2. Also, the optimal dual solution is y1=0, y2=10, and y3=10. Answer the
following questions:
30
[43]
6.
to
2
a) Suppose we changed the elements of the column x2 from
dose the optimal
[2/3]
solution remains optimal? justify your answer
[15]
b) Suppose we add new activity x4 to the problem, and we add of the x4 column
1
to the
1
1
problem, dose the current basis remains optimal? justify your answer
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