sol9 - + x 22 + x 23 + x 24 + x 25 )+ 60( x 31 + x 32 + x...

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AMS 341 Spring, 2011 Homework Set # 9 — Solution Notes #2, 9.2: x i : tons of water processed at site i y i = 1 if Pollution Control Station is built at Site i , 0 otherwise min z = 100000 y 1 + 60000 y 2 + 40000 y 3 + 20 x 1 + 30 x 2 + 40 x 3 s . t . 0 . 4 x 1 + 0 . 25 x 2 + 0 . 20 x 3 80000 0 . 3 x 1 + 0 . 20 x 2 + 0 . 25 x 3 50000 x 1 My 1 x 2 My 2 x 3 My 3 x i 0 and y i = 1 , 0 M = 1 0 . 2 * 80000 = 400000 will do. This follows since at most 400000 tons of water must be processed to remove the required pollutants. #24 review chapter 9: DeFne variables x it = 1 if plant i is built at the start of year t and x it = 0 if not. min z = 20 5 t =1 x 1 t + 16 5 t =1 x 2 t + 18 5 t =1 x 3 t + 14 5 t =1 x 4 t + 7 . 5 x 11 + 6 x 12 + 4 . 5 x 13 + 3 x 14 + 1 . 5 x 15 + 4 x 21 + 3 . 2 x 22 + 2 . 4 x 23 + 1 . 6 x 24 + 0 . 8 x 25 + 6 . 5 x 31 + 5 . 2 x 32 + 3 . 9 x 33 + 2 . 6 x 34 + 1 . 3 x 35 + 3 x 41 + 2 . 4 x 42 + 1 . 8 x 43 + 1 . 2 x 44 + 0 . 6 x 45 s . t . 5 t =1 x 1 t 1 5 t =1 x 2 t 1 5 t =1 x 3 t 1 5 t =1 x 4 t 1 70 x 11 + 50 x 21 + 60 x 31 + 40 x 41 80 year 1 demand 70( x 11 + x 12 ) + 50( x 21 + x 22 ) + 60( x 31 + x 32 ) + 40( x 41 + x 42 ) 100 year 2 demand 70( x 11 + x 12 + x 13 ) + 50( x 21 + x 22 + x 23 )+ 60( x 31 + x 32 + x 33 ) + 40( x 41 + x 42 + x 43 ) 120 year 3 demand 70( x 11 + x 12 + x 13 + x 14 ) + 50( x 21 + x 22 + x 23 + x 24 )+ 60( x 31 + x 32 + x 33 + x 34 ) + 40( x 41 + x 42 + x 43 + x 44 ) 140 year 4 demand 70( x 11 + x 12 + x 13 + x 14 + x 15 ) + 50( x 21
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Unformatted text preview: + x 22 + x 23 + x 24 + x 25 )+ 60( x 31 + x 32 + x 33 + x 34 + x 35 ) + 40( x 41 + x 42 + x 43 + x 44 + x 45 ) 160 year 5 demand x it = 1 , #7, 9.3: Subproblem 1(LP solution): z = 91 3 , x 1 = 13 3 , x 2 = 0 Subproblem 2(Subproblem 1 and x 1 4): z = 29 . 5 , x 1 = 4 , x 2 = 0 . 5 Subproblem 3(Subproblem 1 and x 1 5): INEASIBLE. Subproblem 4(Subproblem 2 and x 2 0): z = 28 , x 1 = 4 x 2 = 0 Subproblem 5(Subproblem 2 and x 2 1): z = 86 3 , x 1 = 11 3 , x 2 = 1 Optimal solution: z = 28 , x 1 = 4 , x 2 = 0 #3, 9.8: The second contraint: x 2 + 1 3 s 1 + 1 6 s 2 = 5 2 , which is equivalent to x 2-2 = 1 2-1 3 s 1-1 6 s 2 Therefore the cut is 1 2-1 3 s 1-1 6 s 2 0....
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sol9 - + x 22 + x 23 + x 24 + x 25 )+ 60( x 31 + x 32 + x...

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