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# ps5 - Massachusetts Institute of Technology 6.854J/18.415J...

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Massachusetts Institute of Technology Handout 9 6.854J/18.415J: Advanced Algorithms Wednesday, October 9, 2009 David Karger Problem Set 5 Due: Wednesday, October 16, 2009. Collaboration policy: collaboration is strongly encouraged . However, remember that 1. You must write up your own solutions, independently. 2. You must record the name of every collaborator. 3. You must actually participate in solving all the problems. This is difficult in very large groups, so you should keep your collaboration groups limited to 3 or 4 people in a given week. 4. No bibles. This includes solutions posted to problems in previous years. Problem 1. Linear Programming By Hand. Consider the following linear programming problem: minimize cx s.t. x 1 + x 2 1 x 1 + 2 x 2 3 x 1 0 x 2 0 x 3 0 For each of the following objectives c , give the optimum value and the set of optimum solutions: (a) c = ( - 1 , 0 , 0) (b) c = (0 , 1 , 0) (c) c = (0 , 0 , - 1) Problem 2. You work for the Short-Term Capital Management company and start the day with D dollars. Your goal is to convert them to Yen through a series of currency trades involving assorted currencies, so as to maximize the amount of Yen you end up with. You are given a list of pending orders: client i is willing to convert up to u i units of currency a i into currency b i at a rate of r i

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ps5 - Massachusetts Institute of Technology 6.854J/18.415J...

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