Consider the following all-integer linear program. 1x₁ + 1x₂ 5x₁ + 7x₂ ≤ 47 1x₁ + 6x₂ ≤ 24 2x₁ + 1x₂ ≤ 17 X₁, X₂20 and integer (a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. 8 X₂ 6 8 x2 8 X2 6 Max s.t. 2 4 6 6 (c) Find the optimal integer solution. at (x₁, x₂) = 6 (b) Solve the LP Relaxation of this problem. at (x₁, x₂) = 8 8 X1 -X1 8 (i)
Consider the following all-integer linear program. 1x₁ + 1x₂ 5x₁ + 7x₂ ≤ 47 1x₁ + 6x₂ ≤ 24 2x₁ + 1x₂ ≤ 17 X₁, X₂20 and integer (a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. 8 X₂ 6 8 x2 8 X2 6 Max s.t. 2 4 6 6 (c) Find the optimal integer solution. at (x₁, x₂) = 6 (b) Solve the LP Relaxation of this problem. at (x₁, x₂) = 8 8 X1 -X1 8 (i)
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 all-integer linear program.
1x₁ + 1x₂
2x₁ + 1x₂ ≤ 17
X₁ X₂20 and integer
(a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.
X2
8
X2
6
8
8
6
X2
6
Max
s.t.
5x₁ + 7x₂ ≤ 47
1x₁ + 6x₂ ≤ 24
X2
4
4
6
at (x₁, x₂) =
6
6
(b) Solve the LP Relaxation of this problem.
(c) Find the optimal integer solution.
at (x₁, x₂) = 1
6
8
8
8
8
X1
(i)
X1
i
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