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The management of a large store wishes to add a fenced-in storage yard of 20,000 square feet, using the building as one side of the yard. Find the minimum amount of fencing that must be used to enclose the remaining 3 sides of the yard.

Respuesta :

Answer:

minimum fencing = 400

Explanation:

area = xy

20000 =xy

[tex]y =\frac{20000}{x}[/tex]

total fencing = x+y+y

[tex]= x+2(\frac{20000}{x}[/tex]

[tex] = x +\frac{40000}{x}[/tex]

now for minimum fencing

[tex]\frac{d}{dx}c = \frac{d}{dx}(x +\frac{40000}{x}) = 0[/tex]

after solving we get

x = 200

therefore

y = 100

minimum fencing  = x +2y

                               = 200+2*100 = 400

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