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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
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 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
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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