Suppose you can buy garden fencing in lengths of 50 feet at the local hardware store. A. If you bought 100 feet of fencing and w
ish to enclose a rectangular garden in your backyard, what should be the dimensions of your garden in order to maximize area?
1 answer:
Answer:
The answer is below
Step-by-step explanation:
Let the length of the rectangular area be L and W be the width of the rectangular garden hence:
Perimeter = 2(L + W)
There is 100 feet of fencing available which represents the perimeter, therefore:
100 = 2(L + W)
L + W = 100/2
L + W = 50
L = 50 - W
The area (A) = L × W
A = L × W
A = (50 - W) × W
A = 50W - W²
To get maximum area, we find the first derivative of the area and equate to zero
A' = 50 - 2W
50 - 2W = 0
2W = 50
W = 50/2
W = 25 feet
100 = 2(L + W)
50 = L + W
L = 50 - W = 50 - 25
L = 25 feet
To maximize area, the length and width should be 25 feet each
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Step-by-step explanation:
Use the formula with n=3.
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