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# t3feeds - 1 U.S dollar buys 0.75 British pounds 1 British...

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COT 5405, Test 3 Duration - 90 mins, 2 Problems 1. (10 points) N jobs are to be processed. Two machines A and B are available. If job i processed on machines A ,then a i units of processing time are needed. If it is processed on machine B ,then b i units of processing time are needed. Because of the peculiarities of the jobs and the machines, it is quite pos- sible that a i b i for some i while a j <b j for some j, j 6 = i .O b t a i

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2. (10 points) Arbitrage is the use of discrepancies in currency exchange rates to make a proFt. ±or example, there may be a small window of time during which
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Unformatted text preview: 1 U.S dollar buys 0.75 British pounds, 1 British pound buys 2 Australian dollars, and 1 Australian dollar buys 0.70 U.S dollars. Then, a smart trader can trade one U.S dollar and end up with 0.75*2*0.7=1.05 U.S dol-lars, a proFt of 5Suppose that there are n currencies C 1 ,...C n and an n × n table R of exchange rates, such that one unit of currency C i buys R [ i,j ] units of currency C j . Devise and analyze a dynamic programming algo-rithm to determine the maximum value of R [ C 1 ,C i (1)] ∗ R [ C i (1) ,C i (2)] ∗ ... ∗ R [ C i ( k ) ,C 1 ] where i (1) ,...,i ( k ) is a subset of { 1 ,...,n } . State and prove time complexity of your algorithm. 2...
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t3feeds - 1 U.S dollar buys 0.75 British pounds 1 British...

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