SOLUTION: Calculus:
A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and ​$2 per foot fo
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Question 1029100: Calculus:
A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and $2 per foot for the other two sides.
Find the cost of the least expensive fence.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and $2 per foot for the other two sides.
Find the cost of the least expensive fence.
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Area:: w*h = 5000
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Cost = 2(h + 2w)
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Substitute for h::
C(w) = 2(5000/w + 2w)
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C(w) = 10,000/w + 4w
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Take the derivative:
C'(w) = 10000(-1/w^2) + 4
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Solve:: -10000/w^2 = -4
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w^2 = 2500
width = 50 ft ; so cost is 2*($2)50 = $200
height = 5000/50 = 100 ft ; so cost is 2($1)100 = $200
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Total cost = $400.00
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Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You are asked to minimize expense
Let = the length of one of the sides
that face north and south and costs $1 / ft
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Let = area enclosed by fences
So, the sides are and
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Let = the perimeter of the area fenced in
The perimeter of the area is:
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Let = the cost of fencing in the area
Set the 1st derivative,
and
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Plug these results back into original equation
The least expensive fence costs $400
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check answer:
OK -here's the plot of Cost, and
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