problemset7_soln - ORIE 3300/5300 Prof. Bland Problem Set 7...

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ORIE 3300/5300 Fall 2011 Prof. Bland Problem Set 7 Solutions 2.(a). An algebraic model for this problem is: 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 14000 9 x 1 + 15 x 2 + 15 x 3 10500 x 1 + x 2 + x 3 700 14 x 1 + 16 x 2 + 23 x 3 - T Θ x 1 , x 2 , x 3 , T 0 There are feasible solutions ( x 1 ,x 2 ,x 3 ,T ) with T > max { 0 , 14 x 1 + 16 x 2 + 23 x 3 - Θ } . (1) However, these solutions cannot be optimal. For any solution ( x 1 ,x 2 ,x 3 ,T ) such that (1) holds, the solution ( x 1 ,x 2 ,x 3 , max { 0 , 14 x 1 + 16 x 2 + 23 x 3 - Θ } ) is also feasible and has higher objective value, because ρ > 0 and T has decreased. So, all optimal solutions ( x * ,T * ) have T * = max { 0 , 14 x * 1 + 16 x * 2 + 23 x * 3 - Θ } . 2.(b). The AMPL model file is: 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; #***************** 1
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param voltaxthreshold; # carbon tax paid for MWH used in excess of taxthreshold param voltaxrate; # carbon tax rate (in dollars per MWH) var Taxedpower >= 0; # power usage in excess of taxthreshold (in MWH) var Make{p in PROD}>=0; #units produced maximize net_revenue: sum{p in PROD} revenue[p]*Make[p] - voltaxrate*Taxedpower;
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problemset7_soln - ORIE 3300/5300 Prof. Bland Problem Set 7...

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