sol8 - AMS 341 Spring, 2010 Homework Set # 8 Solution Notes...

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AMS 341 Spring, 2010 Homework Set # 8 — Solution Notes #2, 7.5: The assignment problem is given by the table (all “supplies” and “demands” are 1). We can also phrase it as an LP as follows: x ij = 1: swimmer i is assigned to stroke j x ij = 0: otherwise min z = 54 x 11 + 54 x 12 + 51 x 13 + 53 x 14 + 51 x 21 + 57 x 22 + 52 x 23 + 52 x 24 + 50 x 31 + 53 x 32 + 54 x 33 + 56 x 34 + 56 x 41 + 54 x 42 + 55 x 43 + 53 x 44 s . t . x 11 + x 12 + x 13 + x 14 = 1 x 21 + x 22 + x 23 + x 24 = 1 x 31 + x 32 + x 33 + x 34 = 1 x 41 + x 42 + x 43 + x 44 = 1 x 11 + x 21 + x 31 + x 41 = 1 x 12 + x 22 + x 32 + x 42 = 1 x 13 + x 23 + x 33 + x 43 = 1 x 14 + x 24 + x 34 + x 44 = 1 x ij = 0 x ij = 1 Since the numbers of rows and columns are equal, we can use the Hungarian method directly. Subtracting the smallest element of each row, we get: 3 3 0 2 0 6 1 1 0 3 4 6 3 1 2 0 Subtracting the smallest element of each column, we get: 3 2 0 2 0 5 1 1 0 2 4 6 3 0 2 0
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sol8 - AMS 341 Spring, 2010 Homework Set # 8 Solution Notes...

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