DMOR-Midterm-04 -...

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Unformatted text preview: UF-ESI-6314204be18ecfd6b68601feb157f4e7d43d4bd5b7d2.xls Problem Statementpage 1 of 11package page _ of __Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435Question 4 (25 points): RowBasis VRSzRHSRatioz1.000.000.000.00ab3.00e10.001.000.000.00c2.00 -3.00d20.000.001.000.00 -4.001.004.002.0030.000.000.001.00 -1.003.001.003.00Marginal Net GainPivot ColumnSuppose that I have optimized some maximizationproblem by the simplex method, and have obtained the following tableau. The values a, b, c, d, and ein the tableau are parameters that I have not specified.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.Hint:Be careful when you say something like "ais positive" or "a> 0." If you mean strictly positive, then that's fine. But there’s a difference between "a≥ 0" and "a> 0." For instance, if I asked, "When is this a feasible solution?" the answer would be "d≥ 0" not "d> 0."x1x2x3x4x5x6PivotRowx1x2x3UF-ESI-6314204be18ecfd6b68601feb157f4e7d43d4bd5b7d2.xls Part Apage 2 of 11package page _ of __Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435Tableau 1RowBasis VRSzRHSRatioz1.000.000.000.00ab3.00e10.001.000.000.00c2.00 -3.00d20.000.001.000.00 -4.001.004.002.0030.000.000.001.00 -1.003.001.003.00Marginal Net GainPivot ColumnOtherwise, the tableau would generate a pivot column and drive another iteration.To assure this tableau remains optimal, these variables must remain nonnegative.a≥b≥Part A (4 points): For what values of aand bis this an optimal tableau? (Assume d≥ 0.) x1x2x3x4x5x6PivotRowx1x2x3By the rules of optimization, the marginal net gainmust remain either zero or negative in that row of the tableau.UF-ESI-6314204be18ecfd6b68601feb157f4e7d43d4bd5b7d2.xls Part Bpage 3 of 11package page _ of __Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435RowBasis VRSzRHSRatioz1.000.000.000.00ab3.00e10.001.000.000.00c2.00 -3.00d20.000.001.000.00 -4.001.004.002.00-0.5030.000.000.001.00 -1.003.001.003.00-3.00Marginal Net Gain-a-b-3.00Pivot Column↑Therefore, Tableau 2 becomes unbounded under the following conditions.a<b>ac<Part B (4 points): For what values of a, b, and ccan we say that this problem is unbounded by looking at the current tableau? (You again need to have d≥ 0.) If a parameter can take any value, please say so....
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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.

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DMOR-Midterm-04 -...

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