hw4sol - CO350 Homework 4 Solutions Winter 2007 Students...

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Students may use either the Simplex Method with tableaus or the Revised Simplex Method. 1. Simplex Method (a) After converting (P) to standard equality form we can construct a tableau with basis B = { 4 , 5 , 6 } . z - 4 x 1 - 2 x 2 - 6 x 3 = 0 3 x 1 + 2 x 2 + x 4 = 10 x 2 + 2 x 3 + x 5 = 8 2 x 1 + x 2 + x 3 + x 6 = 8 Entering variable: x 3 . t = min {- , 8 2 , 8 1 } = 4. Leaving variable: x 5 . Pivoting gives: z - 4 x 1 + x 2 + 3 x 5 = 24 3 x 1 + 2 x 2 + x 4 = 10 1 2 x 2 + x 3 + 1 2 x 5 = 4 2 x 1 + 1 2 x 2 - 1 2 x 5 + x 6 = 4 Entering variable: x 1 . t = min { 10 3 , - , 4 2 } = 2. Leaving variable: x 6 . Pivoting gives: z + 2 x 2 + 2 x 5 + 2 x 6 = 32 + 5 4 x 2 + x 4 3 4 x 5 - 3 2 x 6 = 4 1 2 x 2 + x 3 + 1 2 x 5 = 4 x 1 + 1 4 x 2 - 1 4 x 5 + 1 2 x 6 = 2 Since ¯ c j < 0 for all j N , this is an optimal tableau. The optimal solution for the original problem P is x = [2 0 4] T . The optimal value is 32. (b) The dual (D) of (P) is:
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hw4sol - CO350 Homework 4 Solutions Winter 2007 Students...

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