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CH10 - 1 Chapter 10 MP Solutions SECTION 10.1 SOLUTIONS 1...

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Chapter 10 MP Solutions SECTION 10.1 SOLUTIONS 1.  max z = 3x 1  + x 2  + x 3  s.t.   x 1  + x 2  + x 3  + s 1  = 6        2x 1  - x 3  + s 2  = 4         x 2  + x 3  + s 3  = 2           x 1 ,x 2 ,x 3  >  0     BV(0) = {s 1 , s 2 , s 3 }             NBV(0) = {x 1 , x 2 , x 3 }      1 0 0 0 1 0 0 0 1 0 1 0 B B   c BV  = [0  0  0]                                 c BV  B 0 -1  = [0  0  0]                c 1  = [0  0  0]  0 2 1  -3 = -3                                              c 2  = [0  0  0]  1 0 1    -1 = -1                                          c 3  = [0  0  0]  1 1 1  -1 = -1                                                        Column for x 1  =   1 0 0 0 1 0 0 0 1   0 2 1  =  0 2 1                                                             Right Hand Side =   1 0 0 0 1 0 0 0 1   2 4 6  =   2 4 6                        1
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                      BV(1) = {s 1 , x 1 , s 3 }       NBV(1) = {x 2 , x 3 , s 2 }                                              B 1 -1  =  1 0 0 0 2 / 1 0 0 2 / 1 1 c BV B 1 -1 =[0  3  0]  1 0 0 0 2 / 1 0 0 2 / 1 0  =  [0  3/2  0]                                                                         c 2  = [0  3/2  0]  1 0 1   -1 = -1 c for s 2  = 3/2                      _                    c 3  = [0  3/2  0]   1 1 1  -1 = -5/2                       Column for x 3  =  1 0 0 0 2 / 1 0 0 2 / 1 1    1 1 1  =  1 2 / 1 2 / 3                                                         Right Hand side tableau 1 =   1 0 0 0 2 / 1 0 0 2 / 1 1   2 4 6  =  2 2 4
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