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Stor. Assign. 8

# Stor. Assign. 8 - Min cost=x1(100 x2(125 x3(75 x4(150 x5(80...

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1. Decision variables: let x1 be a binary variable where we build a factory at site 1 (x1=1), or we don’t (x1=0). Similarly for x2, x3, x4, x5, and x6. Max. profit=x1(60) + x2(50) + x3(17) + x4(25) + x5(30) + x6(40) Subject to: x1(30) + x2(40) + x3(10) + x4(16) + x5(18) + x6(32) <=140 (max. investing) x2(40) + x3(10) + x4(16) <=40 (max. investing for x2, x3, and x4) x3 + x5 + x6 >=2 (at least 2 of x3, x5, and x6 must be made) x1 + x5 >=1 (at least 1 of x1 and x5 must be made) x4 <= x6 (if you invest in x4, you must also invest in x6) all variables binary 2. Decision variables: let x1 be a binary variable where we open cart at site 1 (x1=1), or we don’t (x1=0). Similarly for x2, x3, x4, x5, and x6.

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Unformatted text preview: Min. cost=x1(100) + x2(125) + x3(75) + x4(150) + x5(80) + x6(130) Subject to: x1 + x2 + x4 + x5 >=1 (region 1) x2 + x3 + x6 >=1 (region 2) x1 + x4 + x6 >=1 (region 3) x2 + x5 >=1 (region 4) x1 + x3 + x6 >=1 (region 5) x3 + x5 >=1 (region 6) x1 + x4 >=1 (region 7) x2 + x4 + x6 >=1 (region 8) If Jack decides that at most 2 of the sites 1, 2, and 3 can be established, and if site 2 is established then site 6 must be as well, then these extra constraints are added: x1 + x2 + x3 <= 2 (at most 2 of the sites 1, 2, and 3 can be established) x2 <= x6 (if site 2 is established then site 6 must be as well) all variables binary...
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Stor. Assign. 8 - Min cost=x1(100 x2(125 x3(75 x4(150 x5(80...

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