# sol1 - policemen who work 18 hours and begin during shift i...

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AMS 341 Spring, 2011 Homework Set # 1 — Solution Notes #3, 3.3: x2 x1 The LP is unbounded. #4, 3.4: Let x i be the number of days Goldilocks spends in mine i . min z = x 1 + x 2 s . t . 2 x 1 + x 2 12 2 x 1 + 3 x 2 18 x 1 , x 2 0 Graphing the problem, we Fnd the optimal solution is x 1 = 4 . 5, x 2 = 3, z = 7 . 5. #6, 3.5: Let x i be the number of policemen who work for 12 hours and begin during shift i , y i be the number of
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Unformatted text preview: policemen who work 18 hours and begin during shift i . min z = 48( x 1 + x 2 + x 3 + x 4 ) + 84( y 1 + y 2 + y 3 + y 4 ) s . t . x 1 + x 4 + y 1 + y 3 + y 4 ≥ 12 x 1 + x 2 + y 1 + y 2 + y 4 ≥ 8 x 2 + x 3 + y 3 + y 1 + y 2 ≥ 6 x 3 + x 4 + y 2 + y 4 + y 3 ≥ 15 all variables ≥...
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