A rancher has 800 feet of fencing to enclose two adjacent rectangular corrals (see figure)
Question
Answer:
I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.PLEASE SEE ATTACHED IMAGE.
The perimeter is given by:
P = 2 (2x) + 2 (y)
Rewriting we have:
P = 4x + 2y
Substituting:
800 = 4x + 2y
The area is:
A = 2x * y
We write the area as a function of x:
A (x) = 2x * (400-2x)
Rewriting:
A (x) = 800x-4x ^ 2
We derive:
A '(x) = 800-8x
We match zero:
0 = 800-8x
We clear x:
x = 800/8
x = 100 feet
We check that it is a maximum. For this, we look for the second derivative:
A '' (x) = - 8
We evaluate x = 100
A '' (100) = - 8 <0 (is a maximum)
We look for the other dimension:
y = 400-2x
y = 400-2 (100)
y = 400-200
y = 200 feet
Answer:
The dimensions that should be used are that the enclosed area will be a maximum are:
x = 100 feet
y = 200 feet
solved
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11 months ago
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