Hw11_solution

Hw11_solution - = = 1 2 subproblem 4 9.40 1 1.80 z x x = =...

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Introduction to Mathematical Programming IEOR 3608 Prof. Maria Chudnovky Homework #12 Solution 1 We define 1 If i th player is chosen 0 otherwise 1,2,. ..,7 i x i = = 1 2 3 4 5 6 7 1 3 5 7 3 4 5 6 7 2 4 6 7 1 2 3 4 5 6 7 1 7 1 2 3 4 5 6 7 1 1 2 3 4 max 3 2 2 3 3 x 4 . . constraint 1 2 x 1 3 2 2 3 3 3 2 constraint 2 3 3 3 3 2 2 3 2 3 i i i i z x x x x x x x x x x s t x x x x x x x x x x x x x x x x x x x x x x x x x x x = = = + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + { 7 5 6 7 1 3 6 1 4 1 5 2 3 3 2 2 2 constraint 3 1 constraint 4 1 constraint 5 , 0 or 1 i=1,2,. ..7 i i i x x x x x x x x x x x y x y x y = + + + + ≥ - =
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2 We define 1 2 number of product 1 produced number of product 2 produced x x = = 1 2 1 If product 1 is produced 0 otherwise 1 If product 2 is produced 0 otherwise y y = = 1 2 1 2 1 2 1 1 2 2 1 2 1 2 1 2 max 2 5 10 20 . . 3 6 120 120 120 , 0; , integer y , 0 or 1 z x x y y s t x x x y x y x x x x y = + - - + = 3 So the optimal solution is 1 2 20 4 0 z x x = = = 1 2 subproblem 3 19 3 2 Candidate solution z x x = = = 1 4 x 1 3 x t=1 t=3 1 2 subproblem 1 20.5 3.5 1.5 z x x = = = 1 2 subproblem 2 20 4 0 Candidate solution z x x = = = t=2
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4 subproblem 2 Infeasible 1 2 subproblem 3 9.50 0.88 2 z x x =
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Unformatted text preview: = = 1 2 subproblem 4 9.40 1 1.80 z x x = = = 1 2 subproblem 5 6 2 Candidate solution z x x = = = subproblem 6 Infeasible 1 2 subproblem 7 9 1.5 1 z x x = = = 1 2 subproblem 8 8.6 2 0.2 z x x = = = 1 2 subproblem 9 7 1 1 Candidate solution z x x = = = subproblem 10 Infeasible 1 2 subproblem 11 8.5 2.13 z x x = = = 2 3 x 2 2 x 1 1 x 1 x 2 2 x 2 1 x 1 2 x 1 1 x 2 1 x 2 x 1 3 x 1 2 x t=1 t=3 t=4 t=5 t=6 t=7 t=12 t=8 t=9 t=10 t=11 1 2 subproblem 1 9.85 0.44 2.69 z x x = = = subproblem 12 Infeasible 1 2 subproblem 13 8 2 Candidate solution z x x = = = t=2 t=13 So the optimal solution is 1 2 8 2 z x x = = =...
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Hw11_solution - = = 1 2 subproblem 4 9.40 1 1.80 z x x = =...

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