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 Ⓒ
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 Ⓒ
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.4: More Quadratic Functions And Applications
Problem 59PS
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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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