Consider the following all-integer linear program. 1x, 1x₂ 4x₂ + 7x₂ S 27 1x₁ + 6x₂ 5 18 2x₁ + 1x₂ 5 11 X₁, X₂20 and integer. (a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. X2 X2 8 6 Max s.t. 2 2 6 (b) Solve the LP Relaxation of this problem. ] at (x₁, x₂) = ([ (c) Find the optimal integer solution. ] at (x₁, x₂) = ( [ 8 X₁ 8 6 2 4 6 8 X₂ X2 8 6 4 2 4 6 8 X₁ X2 8 @O 2 6 8 X₁ Ⓒ

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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Consider the following all-integer linear program.
1x₁ + 1x₂
4x₁ + 7x₂ ≤ 27
1x₁ + 6x₂ ≤ 18
2x₁ + 1x₂ ≤ 11
X₁, X₂20 and integer
(a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.
X2
X2
8
6
4
Max
s.t.
2
2
4
6
(b) Solve the LP Relaxation of this problem.
at (x₁, x₂) = |
1'
(c) Find the optimal integer solution.
at (x₁, x₂) = |
8
X₁
8
6
4
2
4
6
8
X1
X₂
8
6
4
2
2
4
6
8
X₁
X2
8
6
24
2
4
6
8
X1
Transcribed Image Text:Consider the following all-integer linear program. 1x₁ + 1x₂ 4x₁ + 7x₂ ≤ 27 1x₁ + 6x₂ ≤ 18 2x₁ + 1x₂ ≤ 11 X₁, X₂20 and integer (a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. X2 X2 8 6 4 Max s.t. 2 2 4 6 (b) Solve the LP Relaxation of this problem. at (x₁, x₂) = | 1' (c) Find the optimal integer solution. at (x₁, x₂) = | 8 X₁ 8 6 4 2 4 6 8 X1 X₂ 8 6 4 2 2 4 6 8 X₁ X2 8 6 24 2 4 6 8 X1
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