Posted by **kieran** on Wednesday, September 26, 2012 at 9:54pm.

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.

Dont really know Where to start with this one.

- Calculus -
**Steve**, Thursday, September 27, 2012 at 10:51am
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)

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