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Unformatted text preview: UF-ESI-63142b0675008ba39cf80e2625a51083cbab571de9c5.xls Problem Statementpage 1 of 6package page _ of _Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435Question 5 (20 points): Tableau 1RowBasiszRHSRatioz1.00-5.000.000.00-4.000.00-3.00-25.0010.002.001.000.004.000.00-3.004.0020.00-2.000.000.00-4.001.004.002.0030.002.000.001.00-1.000.00-3.003.00Marginal Net GainPivot ColumnSuppose that I have optimized some minimization problem by the simplex method, and have obtained the following tableau. The last three columns initially correspond to slacks for ≤constraints.Warning: For this question, you must show me the work or rationale you used to arrive to your answer. No credit is given for simply writing the answer.x1x2x3x4x5x6PivotRowx2x5x3UF-ESI-63142b0675008ba39cf80e2625a51083cbab571de9c5.xls Part Apage 2 of 6package page _ of _Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435Constraints rely on slacks and so the shadow prices arise from the currentslacks in the optimal tableau.Part A (4 points):What are the shadow prices?According to Introduction to Mathematical Programmingpage 230:"[We] define the shadow pricefor the ith constraint of an LP to be the amount by which the optimal z-value is improved [...] if the right-hand side of the ith constraint is increased by 1. This definition applies only if the change in the right-hand side of Constraint ileaves the current basis optimal.These are ≤ constraints, so:The shadow price for constraint 1 is -4.The shadow price for constraint 2 is 0....
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This note was uploaded on 02/25/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.
- Fall '09