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# Lab 3 - UniversityofToronto MIE376: Winter2011 1...

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University of Toronto Department of Mechanical and Industrial Engineering MIE376: Mathematical Programming Winter 2011 Lab 3 – Sensitivity Analysis and Duality We can read the sensitivity analysis values from the models we load into AMPL: 1. Load the Model and Data First load the model and data into AMPL. The rest of the lab will address the following Linear Program: max ݔ ൅2ݔ subject to: ݔ ൅3ݔ ൑16 ݔ ൅ݔ ൑7 ݔ ൒0 In AMPL: Solve the LP in AMPL. 2. Reduced Costs Measures how much the cost in a decision variable needs to change before it enters the basis. ampl: display X1.rc, X2.rc; 3. Shadow Prices Measures how much the objective function will change by when the RHS of a constraint increases by one unit. ampl: display Lathe, Drill; 4. Complementary Slackness It is easy to show complementary slackness: ampl: display X1, X1.rc, X2, X2.rc; ampl: display Lathe.slack, Lathe, Drill.slack, Drill; var X1 >= 0; var X2 >= 0; maximize Profit: X1 + 2*X2; subject to Lathe: X1 + 3*X2 <= 16; subject to Drill: X1 + X2 <= 7;

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Lab 3 - UniversityofToronto MIE376: Winter2011 1...

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