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hwk2 - ORIE 3310/5310 Optimization II Spring 2012 Homework...

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ORIE 3310/5310 Optimization II Spring 2012 Homework # 2 Solutions posted Monday 3/5 at 4:00p.m. Homework quiz in recitation Tuesday, 3/6 – Friday, 3/9. BHM refers to the text ”Applied Mathematical Programming” by Bradley, Hax, and Magnanti (available on the course Blackboard site). 1. Problem #13, BHM Chapter 11. 2. Problem #14, BHM Chapter 11. 3. Problem #15, BHM Chapter 11. 4. Use Dijkstra’s algorithm to solve the example on page 2 of the class notes on dynamic programming. 5. For the example on page 6 of the shortest path notes, change c 42 from 1 to - 6 . Compute the shortest path lengths using Dijkstra’s algorithm. Does the algorithm give the correct solution? Why? (Point out where the validation proof fails in the case of negative edge costs.) 6. Problem #7, BHM Chapter 11. 7. Problem #11, BHM Chapter 11. 8. Problem #16(a), BHM Chapter 11. 9. Problem #19, BHM Chapter 11. 10. For trade among banks, mortgages are packaged in $20 million instruments . In such a package, individ- ual mortgages cannot be subdivided, but the packaging need not be exact. E.g., a group of mortgages
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