Question 1029100
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.