The following linear programming formulation comes from a production problem, where x1 and x2 are the amount of products 1 and 2 to be produced respectively. Maximize Subject to 30X150X2 X12X2 < 12 (resource 1) 4X2 <= 4 (resource 2) 2X1 + 3X2 <= 18 (resource 3) X1 >=0, X2 >=0 (a) What is the dual problem of the above production problem? (b) The optimal solution to the primal production problem is x1=7.5, x2=1. Without solving the dual problem, can you tell what is the dual variable (shadow price) associated with resource 1? Why?
The following linear programming formulation comes from a production problem, where x1 and x2 are the amount of products 1 and 2 to be produced respectively. Maximize Subject to 30X150X2 X12X2 < 12 (resource 1) 4X2 <= 4 (resource 2) 2X1 + 3X2 <= 18 (resource 3) X1 >=0, X2 >=0 (a) What is the dual problem of the above production problem? (b) The optimal solution to the primal production problem is x1=7.5, x2=1. Without solving the dual problem, can you tell what is the dual variable (shadow price) associated with resource 1? Why?
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Transcribed Image Text:The following linear programming formulation comes from a production problem, where
x1 and x2 are the amount of products 1 and 2 to be produced respectively.
Maximize
Subject to
30X150X2
X12X2 < 12 (resource 1)
4X2 <= 4 (resource 2)
2X1 + 3X2 <= 18 (resource 3)
X1 >=0, X2 >=0
(a) What is the dual problem of the above production problem?
(b) The optimal solution to the primal production problem is x1=7.5, x2=1. Without
solving the dual problem, can you tell what is the dual variable (shadow price) associated
with resource 1? Why?
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