SOLUTION: my friend has $828 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $14/foot on one side, and cheaper metal fencing which costs $9 foot o
Question 881296: my friend has $828 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $14/foot on one side, and cheaper metal fencing which costs $9 foot on the other three sides.
What are the dimensions of the garden with the largest area she can enclose.
length for cedar side
width for the other side
What is the largest area that can be enclosed? Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = length of the garden in feet
Let = width of the garden in feet
Let = the area of the garden in ft2
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(1)
(1)
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(2)
from (1):
(1)
(1)
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By substitution:
(2)
(2)
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I can say then:
(2)
The maximum occurs at:
Plug this back into (1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
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The cedar side is 18 ft
The maximum area is 414 ft2
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Here's the plot:
