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) = ( )

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) = ( )

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3BEXP

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Question

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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