SOLUTION: I need help with setting up the function. Thanks.
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 328 feet of fe
Question 668721: I need help with setting up the function. Thanks.
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 328 feet of fencing and doesn’t fence the side along the street, what is the largest area that can be enclosed?
You can put this solution on YOUR website! This is like fencing in a rectangle, then removing one side
Let = the area enclosed
Let = the side parallel to the street
Let = the length of a side perpendicular to the street
The amount of fencing is
(1)
The area enclosed is
(2)
----------------
(1)
By substitution:
(2)
(2)
Because of the minus sign in front of the squared term, the equation
has a maximum and not a minimum
(2)
The maximum occurs halfway between the 2 roots
One root is at
and to find the other root,
Half way between is
and,
and, at the maximum,
(2)
(2)
(2) ft2
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Here's the plot with on the vertical axis
and on the horizontal axis
