Posted by **adina** on Thursday, September 19, 2013 at 12:10am.

Old McDonald has 1000 feet of fencing, and wants to build a pen along the side of his barn that will have two separate areas- one for his pigs, and one for his cows. if only one of the fences is to run parallel to the barn, find the dimensions of the pen that would maximize the area.

- precalc -
**Steve**, Thursday, September 19, 2013 at 12:15am
assuming a rectangular fenced area, let

parallel length = x

area = x(1000-x)/3 = 1/3 (1000x-x^2)

Just figure where the vertex of the parabola is, and that will give you the maximum area.

- precalc -
**adina**, Thursday, September 19, 2013 at 12:39am
where did you get the 1/3 from

- precalc -
**Graham**, Thursday, September 19, 2013 at 2:31am
Assume the length of the fence opposite the barn side is: x.

The remaining (1000-x) feet of fence work is divided into three by the two other sides and the partition. Each being: (1000-x)/3.

The area of the pen is: y = x(1000-x)/3

The area is maximum when the derivative is zero. The derivative is:

y' = (1000-2x)/3

Solve for x when y' = 0.

- precalc -
**Steve**, Thursday, September 19, 2013 at 4:53am
since this was pre-calc, I assumed that calculus was not available. But the parabola's vertex is from back in Algebra I!

## Answer This Question

## Related Questions

- Calculus - A farmer has 120 meters of wire fencing to make enclosures for his ...
- algebra - Ian wants to build a rectangular pen for his animals. One side of the ...
- math - a farmer has enough fencing to build 40 feet of fence. He wishes to build...
- math - Trent wants to build a rectangular pen for his animals. One side of the ...
- Math - Manuel wants to build a rectangular pen for his animals. One side of the ...
- Math: pre calculus - a barn is 150 feet long and 75 feet wide. the owner has 240...
- calculus optimization problem - A farmer has 460 feet of fencing with which to ...
- math - a rectangular pen is to be constructed alongside a barn using 120 feet of...
- Math - Old McDonald has 9 pigs. How can he build 4 pens and place and odd number...
- math - Suppose you want to build an outdoor rectangular pen enclosed by fencing ...

More Related Questions