Explanation Given information: The rectangular swimming pool can be built with an area of 1800 square feet. The requirement is 5-foot-wide decks along either side and 10-foot-wide decks at the two ends. Calculation: If x × y is the dimension of the pool, then the total area of the plot is given by A = ( 20 + y ) ( 10 + x ) The rectangular swimming pool can be built with an area of 1800 square feet. (Given) ⇒ x y = 1800 ⇒ y = 1800 x Therefore, A = ( 20 + 1800 x ) ( 10 + x ) Differentiating with respect to ‘x’, we get A ' = ( − 1800 x 2 ) ( 10 + x ) + ( 20 + 1800 x ) ( 1 ) = − 18000 x 2 − 1800 x + 20 + 1800 x = − 18000 x 2 + 20 Equating A ' = 0 ⇒ − 18000 x 2

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.3, Problem

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The rectangular dimension of the smallest piece of property on which the pool can be built under the given conditions.

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Chapter 4 Solutions

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The rectangular dimension of the smallest piece of property on which the pool can be built under the given conditions.

Solution Summary: The author calculates the rectangular dimension of the smallest piece of property on which the pool can be built under the given conditions.

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To find: The rectangular dimension of the smallest piece of property on which the pool can be built under the given conditions.

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Chapter 4 Solutions

To find:

The rectangular dimension of the smallest piece of property on which the pool can be built under the given conditions.