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answer01 - DSC2003 05/T1 Tutorial 1 J Sun1 Linear...

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DSC2003 05/T1 Tutorial 1 J. Sun 1 Linear Programming Problems 1. Ch.4 Problem 14 (Grafton Metalworks) minimize 27 x 1 + 25 x 2 + 32 x 3 + 22 x 4 + 20 x 5 + 24 x 6 subject to . 19 x 1 + . 43 x 2 + . 17 x 3 + . 20 x 4 + . 12 x 6 . 21 : Metal A constraint . 15 x 1 + . 10 x 2 + . 12 x 4 + . 24 x 5 + . 18 x 6 . 12 : Metal B constraint . 12 x 1 + . 25 x 2 + . 10 x 5 + . 16 x 6 . 07 : Metal C constraint . 3 . 14 x 1 + . 07 x 2 + . 53 x 3 + . 18 x 4 + 0 . 31 x 5 + . 25 x 6 . 65 : Metal D constraint . 60 x 1 + . 85 x 2 + . 70 x 3 + . 50 x 4 + . 65 x 5 + . 71 x 6 = 1 . 00 : Weight of alloy x i 0 , i = 1 , . . . , 6 . where x i stands for the tons of ore i required to make 1 ton of alloy. 2. Ch.4 Problem 20 (Anna Broderick) min . 80 x 1 + 3 . 70 x 2 + 2 . 30 x 3 + . 90 x 4 + . 75 x 5 + . 40 x 6 + . 83 x 7 s.t. 520 x 1 + 500 x 2 + 860 x 3 + 600 x 4 + 50 x 5 + 460 x 6 + 240 x 7 1500 520 x 1 + 500 x 2 + 860 x 3 + 600 x 4 + 50 x 5 + 460 x 6 + 240 x 7 2000 4 . 4 x 1 + 3 . 3 x 2 + . 3 x 3 + 3 . 4 x 4 + . 5 x 5 + 2 . 2 x 6 + . 2 x 7 5 30 x 1 + 5 x 2 + 75 x 3 + 3 x 4 + 10 x 7 20 30 x 1 + 5 x 2 + 75 x 3 + 3 x 4 + 10 x 7 60 17 x 1 + 85 x 2 + 82 x 3 + 10 x 4 + 6 x 5 + 10 x 6 + 16 x 7 30 30 x 4 + 70 x 6 + 22 x 7 40 180 x 1 + 90 x 2 + 350 x 3 + 20 x 7 30 All x i 0 i = 1 , ..., 7 where x i stands for the amount of chicken,..., milk (in pound), respectively.
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