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# hw5 - Homework 5 Due March 3 2009 Exercise 4 page 155 Write...

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Homework 5 Due: March 3, 2009 Exercise 4, page 155 Write the dual for each of the following primal problems: (a) maximize z = - 5 x 1 + 2 x 2 subject to - x 1 + x 2 ≤ - 2 2 x 1 + 3 x 2 5 x 1 , x 2 0 . (b) minimize z = 6 x 1 + 3 x 2 subject to 6 x 1 - 3 x 2 + x 3 2 3 x 1 + 4 x 2 + x 3 5 x 1 , x 2 , x 3 0 . (c) maximize z = x 1 + x 2 subject to 2 x 1 + x 2 = 5 3 x 1 - x 2 = 6 x 1 , x 2 unrestricted . Exercise 5, page 163 : Consider the following LP: maximize z = 2 x 1 + 4 x 2 + 4 x 3 - 3 x 4 subject to x 1 + x 2 + x 3 = 4 x 1 + 4 x 2 + x 4 = 8 x 1 , x 2 , x 3 , x 4 0 . Using x 3 and x 4 as starting variables, the optimal tableau is given as Basic x 1 x 2 x 3 x 4 Solution z 2 0 0 3 16 x 3 0 . 75 0 1 - 0 . 25 2 x 2 0 . 25 1 0 0 . 25 2 Write the associated dual problem and determine its optimal solution in two ways. 1

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Exercise 3(a), Page 167 : Consider the following LP model: maximize z = 3 x 1 + 2 x 2 + 5 x 3 subject to x 1 + 2 x 2 + x 3 + x 4 = 30 3 x 1 + 2 x 3 + x 5 = 60 x 1 + 4 x 2 + x 6 = 20 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 0 . Check the optimality and the feasibility of the following basic solution: Basic variables = ( x 4 , x 3 , x 6 ), and Inverse = 1 - 1 2 0 0 1 2 0 0 0 1 . Exercise 6, page 168 : Consider the following LP model: maximize z = 5 x 1 + 2 x 2 + 3 x 3 subject to x 1 + 5 x 2 + 2 x 3 b 1 x 1 - 5 x 2 - 6 x 3 b 2 x 1 , x 2 , x 3 0 . The following optimal tableau corresponds to specific values of b
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hw5 - Homework 5 Due March 3 2009 Exercise 4 page 155 Write...

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