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Problem Set 2 Solutions

# Problem Set 2 Solutions - ORIE 3300/5300 Optimization I...

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ORIE 3300/5300 Optimization I Homework #2 Solutions Fall 2009 2.(a) An algebraic model: max 2200 x 1 + 2695 x 2 + 3190 x 3 - ρT subject to : 1 . 75 x 1 + 1 . 9 x 2 + 2 x 3 1500 2 x 1 + 2 x 2 + 4 x 3 3000 14 x 1 + 16 x 2 + 23 x 3 14200 9 x 1 + 15 x 2 + 15 x 3 10500 1 x 1 + 1 x 2 + 1 x 3 700 14 x 1 + 16 x 2 + 23 x 3 - T Θ x 1 0 , x 2 0 , x 3 0 , T 0 The feasible region includes points ( x 1 , x 2 , x 3 , T ) with T > max { 0 , 14 x 1 + 16 x 2 + 23 x 3 - Θ } . However, since the objective function coefficient of T is strictly negative, such solutions cannot be optimal. So, all optimal solutions ( x * , T * ) have T * = max { 0 , 14 x * 1 + 16 x * 2 + 23 x * 3 - Θ } . . 2.(b) Model file: set PROD; #products set RESOURCES; #ingredients in scarce supply param avail{RESOURCES}; #amount of each ingredient (in appropriate units) available param revenue{PROD}; #revenue per unit param recipe{RESOURCES,PROD}; #amount (in appropriate units) of each resource needed to produce one unit of product set TAXEDRESOURCE; #***************** param taxthreshold; # carbon tax paid for MWH used in excess of taxthreshold 1

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param taxrate; # carbon tax rate (in dollars per MWH)
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Problem Set 2 Solutions - ORIE 3300/5300 Optimization I...

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