homework-5 - MthSc810 Mathematical Programming Fall 2011,...

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MthSc810 – Mathematical Programming Fall 2011, Homework #5. Due October 4, 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 Solve the following problem (after an appropriate transformation) using the sim- plex method (i.e., do not use dictionaries but rather matrices B, N and vectors c B , c N , d etc.). min 2 x 1 - x 2 s.t. 3 x 1 + x 2 9 x 1 +2 x 2 8 x 1 , x 2 0 . Use B = { 1 , 4 } as the ±rst basis. Problem 2 Consider the following LP problem: min - 3 x 1 - 4 x 2 s.t. x 1 + x 2 0 x 1 +2 x 2 0 x 1 , x 2 0 . Start from the basis B = { 3 , 4 } . 1. Is it a BFS? 2. What is the corresponding objective function value? 3. How many constraints are active at this basic solution? 4. Does it contradict the de±nition of basic (feasible) solution? 5. If this is a BFS, perform at most two iterations of the simplex (i.e., do not perform an iteration if you are at the optimal solution). 6. Does the BFS you found after two iterations correspond to an optimal solu-
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This note was uploaded on 03/14/2012 for the course MTHSC 810 taught by Professor Staff during the Fall '08 term at Clemson.

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homework-5 - MthSc810 Mathematical Programming Fall 2011,...

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