A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. what is the maximum area that the farmer can enclose with 100 ft of fence? what should the dimensions of the garden be to give this area?
Question
Answer:
The perimeter will be:P = 2x + y
100 = 2x + y
The area is:
A = x * y
We write the area as a function of x:
A (x) = x * (100-2x)
Rewriting:
A (x) = 100x - 2x ^ 2
We derive:
A '(x) = 100 - 4x
We equal zero and clear x:
0 = 100 - 4x
4x = 100
x = 25 feet
The other dimension is:
y = 100-2x
y = 100-2 (25)
y = 100-50
y = 50 feet
The area will be:
A = (25) * (50)
A = 1250 feet ^ 2
Answer:
the maximum area that the farmer can enclose with 100 ft of fence is:
A = 1250 feet ^ 2
The dimensions of the garden to give this area should be:
x = 25 feet
y = 50 feet
solved
general
11 months ago
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