HWA05 - Managerial ACG 2071 Spring 2006 Professor Lin...

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Managerial ACG 2071 Professor Lin Spring 2006 Solution to #05 1. The primal: Minimize z 3 + 5z 4 Subject to q z z 4 3 + ( 1 λ ) 4 z 3 ( 2 λ ) (1) The dual is, Maximize 2 1 4 q λ λ Subject to 1 2 1 λ λ (z 1 ) 5 1 λ (z 2 ) (2) Solve both the primal and the dual The Primal The Dual q 2 4 6 8 q 2 4 6 8 Obj 2 4 14 24 Obj 2 4 14 24 z 3 2 4 4 4 1 λ 1 a+5(1-a) for ] 1 , 0 [ a 5 5 z 4 2 4 2 λ 4(1-a) for ] 1 , 0 [ a 4 4 Shadow price for the first constraint 1 a + 5(1-a), for 0<=a<=1 5 5 Shadow price for the first constraint 2 4 4 4 Shadow price for the second constraint 4 4 Shadow price for the second constraint 2 4
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(3) Summarize the findings: (i) for any q, the objective functions of the primal and the dual are the same. (ii) The solution to the primal is the shadow price of the constraints of the dual. (iii) The solution to the dual is the shadow price of the constraints of the primal. (iv)
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HWA05 - Managerial ACG 2071 Spring 2006 Professor Lin...

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