Consider the following IP problem: Minimize Z = 3x1 - 2x2 subject to 5x1 - 7x2 ≥3 X1 ≤ 3 X2 ≤ 3 and x1 ≥0, x2 ≥ 0 are integers. a) Use the MIP branch-and-bound algorithm to solve this model by hand. For each subproblem, solve its LP relaxation graphically.
Consider the following IP problem: Minimize Z = 3x1 - 2x2 subject to 5x1 - 7x2 ≥3 X1 ≤ 3 X2 ≤ 3 and x1 ≥0, x2 ≥ 0 are integers. a) Use the MIP branch-and-bound algorithm to solve this model by hand. For each subproblem, solve its LP relaxation graphically.
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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Transcribed Image Text:Consider the following IP problem:
Minimize Z = 3x₁ - 2x₂
subject to
5x₁ - 7x₂ ≥ 3
x1 ≤ 3
x₂ ≤3
and x₁ ≥ 0, x₂ ≥ 0 are integers.
a)
Use the MIP branch-and-bound algorithm to solve this model by hand. For each
subproblem, solve its LP relaxation graphically.
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Step 1: Analysis and Introduction
VIEWStep 2: Solve the original IP graphically.
VIEWStep 3: Formulate the IP for branch 1 and solve them graphically.
VIEWStep 4: Formulate the IP for subproblem 1 in branch 2 and solve it.
VIEWStep 5: Formulate the IP for subproblem 2 in branch 2 and solve it.
VIEWStep 6: Conclude the optimal solution to the provided MIP.
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