Homework_10_Solutions

Homework_10_Solutions - HOMEWORK 10 SOLUTIONS GRADERS:...

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Unformatted text preview: HOMEWORK 10 SOLUTIONS GRADERS: ANDREW LI (AAL2131, A-I), LINWEI LI (LL2713, J-Q), & LEO LIN (CL2892, R-Z) 1. Problem 1 10 pts Let y ij = 1 if node i colored j 0 otherwise ,i = 1 ,...,n, j = 1 , 2 , 3 minimize 0 subject to: y i 1 + y i 2 + y i 3 = 1 , ∀ i = 1 ,...,n y ij + y kj ≤ 1 ∀ j = 1 , 2 , 3 , ( i,k ) ∈ E y ij ∈ { , 1 } ∀ i = 1 ,...,n, j = 1 , 2 , 3 2. Problem 2 10 pts maximize y 1 + ··· + y n subject to: y i + y j ≤ 1 , ∀ ( i,j ) / ∈ E y i ∈ { , 1 } , ∀ i = 1 ,...,n 3. Problem 3 (a) 4 pts maximize 2 x 11 + 4 x 12 + 8 x 13 + 16 x 14 + 5 x 21 + 10 x 22 + 20 x 23 + 40 x 24 subject to: x 11 + 2 x 12 + 4 x 13 + 8 x 14 + x 21 + 2 x 22 + 4 x 23 + 8 x 24 ≤ 15- x 11- 2 x 12- 4 x 13- 8 x 14 + x 21 + 2 x 22 + 4 x 23 + 8 x 24 ≤ 2 x 11 + 2 x 12 + 4 x 13 + 8 x 14- x 21- 2 x 22- 4 x 23- 8 x 24 ≥ 2 x 11 + 2 x 12 + 4 x 13 + 8 x 14 + x 21 + 2 x 22 + 4 x 23 + 8 x 24 ≥ 2 x ij ∈ { , 1 } , ∀ i = 1 , 2 , j = 1 , 2 , 3 , 4 (b) 2 pts minimize- 2 x 11- 4 x 12- 8 x 13- 16...
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This note was uploaded on 02/08/2012 for the course IEOR 4004 taught by Professor Sethuraman during the Fall '10 term at Columbia.

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Homework_10_Solutions - HOMEWORK 10 SOLUTIONS GRADERS:...

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