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Unformatted text preview: Douglass Houghton Workshop, Section 1, Mon 11/7/11 Worksheet May the Road Rise to Meet You 1. Weve been working on the problem of finding the shortest road network between three cities in the plane. In the case we considered, the three cities were at the corners of a 45 45 90 triangle with legs 10 miles long. The simplest idea is to just build roads along the legs; that makes a network of length 20. By constructing a Yshaped network like the one at the right, we found b b b b A B C 10 10 x The length of the Y network is x + 2 radicalBig 100 20 x cos(45) + x 2 . (a) When x = 0, we have the Vshaped network. Whats the length in that case? (b) Is there a value for x which makes the Y shorter than the V ? (c) What if x is negative? Could we do better than the V that way? (d) Find the best value for x . 2. Let a be some positive constant. Graph f ( x ) = e 1 2 ( ax ) 2 on the board....
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 Winter '08
 Conger
 Critical Point, Optimization, pear tree, road network, golden eggs

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