Posted by **Shelby** on Tuesday, October 30, 2012 at 11:41pm.

A farmer has 120 meters of wire fencing to make enclosures for his pigs and cows. The rectangular enclosure he is considering will have one side up against a barn (in the center of one side that is 150 meters long, so the enclosure won't require fencing along that edge) and a section of fencing perpendicular to the barn, down the middle of the entire enclosure, to keep the pigs and cows separate.

How should the farmer allocate the fencing to the edges of the enclosure to maximize the area inside? That is, for the maximum area enclosure what should be the length of the side of the rectangle perpendicular to the barn and what should be the length of the side of the rectangle parallel to the barn?

- Calculus -
**Steve**, Wednesday, October 31, 2012 at 10:26am
If the length along the bar is x, and the width is y,

x+3y = 150

The area a = xy = (150-3y)y = 3(50y-y^2)

da/dy = 3(50-2y) da/dy=0 when y=25

thus, x = 75

So, the whole area is 75x25

As expected, the area is maximum when the fencing is evenly divided between lengths and widths. For a single fully enclosed area, that would be a square.

## Answer this Question

## Related Questions

- math - a farmer has 120 m of fencing to make two identical rectangular ...
- advanced math - Suppose you have 168 meters of fencing with which to make two ...
- MATH ANALYSIS - How should this be done? Suppose you have 132 m of fencing with ...
- MATH ANALYSIS - How should this be done? Suppose you have 132 m of fencing with ...
- math - Farmer Hodges has 50 feet of fencing to make a rectangular hog pen ...
- calculus optimization problem - A farmer has 460 feet of fencing with which to ...
- Algebra - Suppose a farmer has 120 feet of fencing to make a rectangular ...
- Math - Suppose a farmer has 120 feet of fencing to make a rectangular barnyard ...
- optimization - A farmer wants to make 9 identical rectangular enclosures as ...
- Functions - A farmer wants to enclose a rectangular field with 180m of fencing. ...