# hw7 - Homework 7 Engineering Optimization ISYE 3133 9.2.2...

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Unformatted text preview: Homework 7 Engineering Optimization ISYE 3133 9.2.2 Let x i = Tons of water processed at site i . y i = 1 if Pollution Control Station is built at site i . y i = 0 otherwise. Then the appropriate IP is: Min z = 100 , 000 y 1 + 60 , 000 y 2 + 40 , 000 y 3 + 20 x 1 + 30 x 2 + 40 x 3 s.t. . 40 x 1 + . 25 x 2 + . 20 x 3 ≥ 80 , 000 . 30 x 1 + . 20 x 2 + . 25 x 3 ≥ 50 , 000 x 1 ≤ My 1 x 2 ≤ My 2 x 3 ≤ My 3 All x ij ≥ and all y i = 0 or 1 . M = 80 , 000 20 = 400 , 000 will do. This follows since at most 400,000 tons of water must be processed to remove the required pollutants. 1 9.2.12 Let y 1 = 1 if NY is used, y 2 = 1 if LA is used, y 3 = 1 if Chicago is used, y 4 = 1 if Atlanta is used. Also y i = 0 if city i is not used. Define x ij as the units shipped from the warehouse in city i to region j . Min z = 400 y 1 + 500 y 2 + 300 y 3 + 150 y 4 + 20 x 11 + 40 x 12 + 50 x 13 + 48 x 21 + 15 x 22 + 26 x 23 + 26 x 31 + 35 x 32 + 18 x 33 + 24 x 41 + 50 x 42 + 35 x 43 s.t. x 11 + x 21 + x 31 + x 41 ≥ 80 x 12 + x 22 + x 32 + x 42 ≥ 70 x 13 + x 23 + x 33 + x 43 ≥ 40 x 11 + x 12 + x 13 ≤ 100 y 1 x 21 + x 22 + x 23 ≤ 100 y 2 x 31 + x 32 + x 33 ≤ 100 y 3 x 41...
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hw7 - Homework 7 Engineering Optimization ISYE 3133 9.2.2...

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