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# sol10 - AMS 341 Spring 2010 Homework Set 10 Solution...

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AMS 341 Spring, 2010 Homework Set # 10 — Solution Notes #4, 13.4: Define f i ( c ) = minimum # of crimes committed in precincts i,i + 1 ..., 3 x i ( c ) = # of cars assigned to precinct i in order to get f i ( c ) Then f 3 (0) = 20 , x 3 (0) = 0 , f 3 (1) = 14 , x 3 (1) = 1 , f 3 (2) = 11 , x 3 (2) = 2 , f 3 (3) = 8 , x 3 (3) = 3 , f 3 (4) = 6 , x 3 (4) = 4 , f 3 (5) = 5 , x 3 (5) = 5 , f 2 (0) = 25 + f 3 (0) = 45 , x 2 (0) = 0 , f 2 (1) = min braceleftBigg 25 + f 3 (1) = 39 19 + f 3 (0) = 39 , x 2 (1) = 0 or 1 , f 2 (2) = min 25 + f 3 (2) = 36 19 + f 3 (1) = 33 16 + f 3 (0) = 36 , x 2 (2) = 1 , f 2 (3) = min 25 + f 3 (3) = 33 19 + f 3 (2) = 30 16 + f 3 (1) = 30 14 + f 3 (0) = 34 , x 2 (3) = 1 or 2 , f 2 (4) = min 25 + f 3 (4) = 31 19 + f 3 (3) = 27 16 + f 3 (2) = 27 14 + f 3 (1) = 28 12 + f 3 (0) = 32 , x 2 (4) = 1 or 2 , f 2 (5) = min 25 + f 3 (5) = 30 19 + f 3 (4) = 25 16 + f 3 (3) = 24 14 + f 3 (2) = 25 12 + f 3 (1) = 26 11 + f 3 (0) = 31 , x 2 (5) = 2 , f 1 (5) = min 14 + f 2 (5) = 38 10 + f 2 (4) = 37 7 + f 2 (3) = 37 4 + f 2 (2) = 37 1 + f 2 (1) = 40 0 + f 2 (0) = 45 , x 1 (5) = 1 , 2 or 3 Optimal allocations of patrol cars: Precinct 1 Precinct 2 Precinct 3 Crimes 3 1 1 37 2 2 1 37 2 1 2 37 1 2 2 37 1

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sol10 - AMS 341 Spring 2010 Homework Set 10 Solution...

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