homework-8 - MthSc810 Mathematical Programming Fall 2011...

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MthSc810 – Mathematical Programming Fall 2011, Homework #8. Due Thursday, October 27, 2011, 6PM EDT. From the syllabus: homework will be penalized 50% for each day they are late. After two days, they will not be accepted. No exception. Problem 1. Write the dual of the following problems: 1. The Klee-Minty example for general n ; 2. The bank loan model seen in lecture 2, slide 21; 3. The production planning model (same lecture, slide 11). Problem 2. Consider the following problem: min 6 x 1 + 4 x 2 s.t. x 1 + x 2 = 1 3 x 1 + x 2 0 x 1 0 x 2 0 . 1. Write its dual; 2. Solve the dual with the graphical method; 3. Find an optimal solution of the primal by applying complementary slackness. 4. Verify the primal’s optimal solution by solving the primal through the graph- ical method. Problem 3. Solve the following problem, after writing its standard form, by means of the dual simplex method. Use the initial basis B = { 3 , 4 } . Note that the initial basis is only dual feasible.
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