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s07 - The amount of wire is easily seen to be(d-k(D 2 4x 2...

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Solution to Problem 7 Congratulations to this week’s winner Kevin Bourrillion There were 4 solutions received. Kevin’s was the only one that was both correct and complete. Now to the answer: Let x denote the vertical distance from where the wire is attached to the trees to the point where the descending wire begins. Then x lies in the interval [0,d] with x = 0 corresponding to the "T"--shaped configuration and x = d corresponding to the "V"-shaped configuration.
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Unformatted text preview: The amount of wire is easily seen to be (d-k) + (D 2 + 4x 2 ) 1/2 . Our task is to minimize this quantity over the interval [0,d] . Straightforward differentiation gives a unique local minimum at the point P = (D 2 /12) 1/2 . This local minimum is a global minimum as long as it is a point in the interval in question, i.e. as long as P < d . In the other case the "V"-shaped configuration yields a minimum....
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