Explanation Given data: y The fenced area is to be built along the river at the in an efficient way. The side of the rectangle along the river is twice the other sides and the fencing material is in a fixed amount. Method/Formula used: The area of a rectangle of length (l) and breadth (b) is A = l × b . The function y = f ( x ) is maximum at x = a when f ′ ( a ) = 0 , and f ″ ( a ) < 0 Proof: The efficient way to build a fencing are area is that for a given fencing material the fenced area must be maximum. Let x and y be the breadth and length of the fenced area A then A = x ⋅ y .....(1) Let the fencing material for 3 sides fencing is fixed by an amount M that is 2 x + y = M (Length of fence) = constant. .....(2) Now, from results (1), and (2) A = x ⋅ ( M 2 − x ) = M x 2 − x 2 d A d x = M 2 − 2 x

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.4, Problem 64P

To determine

To prove: That the most efficient way to build a rectangular fenced area along a river is that the side parallel to the river is twice long as the other sides.

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Chapter 3.4, Problem 63P

Chapter 3.4, Problem 1TF

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