- #1

karush

Gold Member

MHB

- 3,269

- 5

A farmer wants to fence an area of $1.5$ million square feet

$(1.5\text{ x }10^6 \text{ ft}^2)$

in an a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?

well, I understand the problem to mean that the fence goes around the perimeter then another fence goes down the middle dividing the area in half. So using the length $l$ as $2$ sides and another fence $l$ length going down the middle then.

total length of fence $\displaystyle f(l) = 3l+\frac{2\cdot 1.5\text{ x }10^6}{l}$

persuming this is correct then $\frac{d}{dl}f(l)=0$ would be $l$ for the min length of fence for that area