I need help with part b and c. Please explain the steps on how to solve. Consider the following all-integer linear program.1x₁ + 1x₂Maxs.t.5x₁ + 6x₂ ≤ 411x₁ + 5x₂ ≤ 202x₁ + 1x₂ ≤ 15X₁, X₂ ≥ 0 and integer (b) Solve the LP Relaxation of this problem.at (x₁, x₂) ==(c) Find the optimal integer solution.= ([at (x₁, x₂) =

Linear programming is a mathematical technique that is also used in operations management…

Answered: Max 1x₁ + 1x2 s.t. 5x₁ + 6x₂ ≤ 41 1x1 +…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 73P

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Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 6x1 + 5x2 ≤ 28 11x1 + 5x2 ≤ 46 x1 + 2x2 ≤ 8 x1, x2 ≥ 0 and integer Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. x1= fill in the blank 2 x2= fill in the blank 3 Optimal Solution to the LP Relaxation fill in the blank 4 Round down to find a feasible integer solution. If your answer is zero enter “0”. x1= fill in the blank 5 x2= fill in the blank 6 Feasible integer solution fill in the blank 7 Find the optimal integer solution. If your answer is zero enter “0”. x1= fill in the blank 8 x2= fill in the blank 9 Optimal Integer Solution fill in the blank 10
Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 6x1 + 5x2 ≤ 28 11x1 + 5x2 ≤ 46 x1 + 2x2 ≤ 8 x1, x2 ≥ 0 and integer Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. x1= fill in the blank 2 x2= fill in the blank 3 Optimal Solution to the LP Relaxation fill in the blank 4 Round down to find a feasible integer solution. If your answer is zero enter “0”. x1= fill in the blank 5 x2= fill in the blank 6 Feasible integer solution fill in the blank 7 Find the optimal integer solution. If your answer is zero enter “0”. x1= fill in the blank 8 x2= fill in the blank 9 Optimal Integer Solution fill in the blank 10 Is it the same as the solution obtained in part (b) by rounding down?
Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 42 1x1 + 5x2 ≤ 20 2x1 + 1x2 ≤ 15 x1, x2 ≥ 0 and integer (b)Solve the LP Relaxation of this problem. ( ) at (x1, x2) = ( )
Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 42 1x1 + 5x2 ≤ 20 2x1 + 1x2 ≤ 15 x1, x2 ≥ 0 and integer (b)Solve the LP Relaxation of this problem. ( ) at (x1, x2) = ( ) (c) Find the optimal integer solution. ( ) at (x1, x2) = ( )
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1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1

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Max 1x₁ + 1x2 s.t. 5x₁ + 6x₂ ≤ 41 1x1 + 5x₂ ≤ 20 2x₁ + 1x₂ ≤ 15 X₁, X₂20 and integer