Lecture16aa - Lecture 2/25/08 Introduction to Linear...

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Lecture 2/25/08 Introduction to Linear Programming 1. Review of Minimization Problem Example 2. Special Cases of LPs
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Data Table for Minimization Problem NITROGEN PHOSPHATE COST Brand (LB./BAG) (LB./BAG) $/BAG Super-gro 2 4 $6 Crop-quick 4 3 $3 Requirement (lbs) 16 24
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LP Formulation Decision Variables Let x 1 = number of bags of Super-Gro Let x 2 = number of bags of Crop-quick Objective Function Minimize 6 x 1 + 3 x 2 Constraints 2 x 1 +4 x 2 ≥ 16 (nitrogen requirement) 4 x 1 +3 x 2 ≥ 24 (phosphorus req’d) x 1 , x 2 ≥o
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Graphical Solution X 1 X 8 4 Nitrogen requirement 8 Phosphorus requirement 6 Feasible Region Level curve: 6 x 1 + 3 x 2 =30 Optimal Soln
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Optimal Solution • X 1 =0, X 2 =8 8 bags of Crop Quick will satisfy nitrogen and phosphorus requirements at minimum cost. Minimum cost value = 6(0) + 3(8) =$24
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Example of Alternate Optimal Solutions MAX: 450X 1 + 300X 2 S.T.: 1X 1 + 1X 2 200 9X 1 + 6X 2 1566 12X 1 + 16X 2 2880 X 1 0 X 2 0
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X 2 X 1 250 200 150 100 50 0 0 50 100 150 200 250 450X 1 + 300X 2 = 78300 Example of Alternate Optimal Solutions objective function level curve alternate optimal solutions
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Lecture16aa - Lecture 2/25/08 Introduction to Linear...

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