Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![Consider the following all-integer linear program.
5X + 8X2
Max
s.t.
8
6x₁ + 5x₂ ≤ 35
11x₁ + 4x₂ ≤ 44
1x₂ + 2x₂ ≤ 12
X₁X₂20 and integer
(a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions.
X2
X2
| at (x₁, x₂) = |
6
(c) Find the optimal integer solution.
at (x₁, x₂) =
8
8
(b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.)
] at (x₁, x₂) = ( [
Using this solution, round down to find a feasible integer solution.
6
Is it the same as the solution obtained in part (b) by rounding down?
O Yes
O No
6
8
X1
X2
8
6
2
2
4
6
8
X1
X2
8
6
4
2
2
6
8
X₁](https://content.bartleby.com/qna-images/question/7969c5f0-e605-40e7-a8e0-a97de5028afc/7dcaadfd-3693-48ff-a1f2-c5c8913f64f8/rmlxm4l_processed.png)
Transcribed Image Text:Consider the following all-integer linear program.
5X + 8X2
Max
s.t.
8
6x₁ + 5x₂ ≤ 35
11x₁ + 4x₂ ≤ 44
1x₂ + 2x₂ ≤ 12
X₁X₂20 and integer
(a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions.
X2
X2
| at (x₁, x₂) = |
6
(c) Find the optimal integer solution.
at (x₁, x₂) =
8
8
(b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.)
] at (x₁, x₂) = ( [
Using this solution, round down to find a feasible integer solution.
6
Is it the same as the solution obtained in part (b) by rounding down?
O Yes
O No
6
8
X1
X2
8
6
2
2
4
6
8
X1
X2
8
6
4
2
2
6
8
X₁
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