# Calculus

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a property owner wants to build a rectangular enclosure around some land that is next to the lot of a neighbor who is willing to pay for half the fence that actually divides the two lots. If the area is A, what should the dimensions of the enclosure be so that the cost to the owner is a minimum.

• Calculus -

if the area enclosed is x by y, and the neighbor will pay for half the cost of the y side,

A = xy
C = 2x + 3/2 y

C = 2x + 3/2 (A/x)
dC/dx = 2 - 3A/(2x^2)
dC/dx = 0 when 3A/(2x^2) = 2
x = √(3A)/2

so, the lot is √(3A)/2 by 2√(A/3)

cost is thus √(3A) + 3/2 * 2√(A/3) = 2√(3A)

• Calculus -

I DON'T GET IT!?

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