2. A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. a) If there are 12 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary. b) If the area is to be 8 km², find the dimension of the rectangle to minimize the amount of fence necessary to enclose the three remaining sides.
2. A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. a) If there are 12 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary. b) If the area is to be 8 km², find the dimension of the rectangle to minimize the amount of fence necessary to enclose the three remaining sides.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.2: The Parallelogram And Kite
Problem 5E: A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If...
Question
Transcribed Image Text:2. A rectangular bird sanctuary is being created with one side along a straight riverbank. The
remaining three sides are to be enclosed with a protective fence.
a) If there are 12 km of fence available, find the dimension of the rectangle to maximize the
area of the sanctuary.
b) If the area is to be 8 km², find the dimension of the rectangle to minimize the amount of
fence necessary to enclose the three remaining sides.
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Step 1: Define the problem
VIEWStep 2: Calculate the area of bird sanctuary in terms of y
VIEWStep 3: Calculate the derivative of A(y)
VIEWStep 4: Calculate the critical values
VIEWStep 5: Calculate the second derivative test and dimensions of maximum area
VIEWStep 6: Calculate the amount of fence for bird sanctuary in terms of x
VIEWStep 7: Calculate the derivative of P(x)
VIEWStep 8: Calculate the critical values
VIEWStep 9: Calculate the second derivative test and dimension for minimize amount of fence
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