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Consider the following all-integer linear program. 5xy + 8x2 Max s.t. 6x₁ + 5x₂ ≤ 35 10x₂ + 4x₂ ≤ 40 1x₁ + 2x₂ ≤ 12 X₁ X₂20 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. X₂

Consider the following all-integer linear program. 5xy + 8x2 Max s.t. 6x₁ + 5x₂ ≤ 35 10x₂ + 4x₂ ≤ 40 1x₁ + 2x₂ ≤ 12 X₁ X₂20 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. X₂

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 46P
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Consider the following all-integer linear program. 5Xq + 8X2 6x₁ + 5x₂ ≤ 35 10x₁ + 4x₂ ≤ 40 1x1 + 2x₂ ≤ 12 X₁, X₂ ≥ 0 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. X2 X2 8 Max s.t. 2 2 4 at (x₁, x₂) = 6 8 (c) Find the optimal integer solution. at (x₁, x₂) X1 8 4 (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. 2 Is it the same as the solution obtained in part (b) by rounding down? Yes No 4 6 8 i X2 8 6 4 2 2 4 6 8 X1 X2 8 4 2 2 4 6 8 X1
Transcribed Image Text:Consider the following all-integer linear program. 5Xq + 8X2 6x₁ + 5x₂ ≤ 35 10x₁ + 4x₂ ≤ 40 1x1 + 2x₂ ≤ 12 X₁, X₂ ≥ 0 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. X2 X2 8 Max s.t. 2 2 4 at (x₁, x₂) = 6 8 (c) Find the optimal integer solution. at (x₁, x₂) X1 8 4 (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. 2 Is it the same as the solution obtained in part (b) by rounding down? Yes No 4 6 8 i X2 8 6 4 2 2 4 6 8 X1 X2 8 4 2 2 4 6 8 X1
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