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p2_sp2011 - PRELIM 2 ORIE 3310/5310 Closed book exam...

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PRELIM 2 ORIE 3310/5310 March 10, 2011 Closed book exam. Justify all work. 1. For an acyclic digraph G = ( V, E ) with V = { 1 , 2 , . . . , n } and edge lengths c ij , ( i, j ) E , we studied the fundamental problem of determining a shortest (1 , n ) -path. (a) (5 points) Give the dynamic programming (DP) solution for this problem; i.e., define an ap- propriate optimal value function, state the recursion which solves the problem, and indicate the sequence in which the recursive equations must be solved. (b) (5 points) Your solution in part (a) depends on the fact that the nodes have been indexed in a manner consistent with the edge orientations. Explain. (c) (10 points) Estimate the (worst-case) computational effort required by your recursion of part (a). (d) (20 points) I am considering the purchase and maintenance costs over a five-year planning horizon for a gPad (a new portable electronic gaming device). The current purchase price for a new gPad is $300 and I estimate (optimistically) that in years to come this price will drop to $280 (in 2012), $260 (in 2013), $250 (in 2014, 2015, and 2016). The maintenance cost for a gPad during its jth
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