posted by .

Farmer John is building a pen to keep his pig in. John has 40m of fencing. He will only need to make 3 sides to the pen because the 4th side will be along a barn. If John wants the maximum area what should the side lengths of the pen be?

L + 2w = 40
so
L = 40 - 2w

A = L * w
A =(40-2 w)(w) = 40 w - 2 w^2

2 w^2 - 40 w = -A
w^2 - 20 w = -A/2

w^2 - 20 W + 100 = -A/2 + 100
(w-10)^2 = -(1/2)(A-200)
vertex at w = 10, A = 200
so L = 20

## Similar Questions

1. ### Math

A rectangular dog pen is to be constructed using a barn wall as one side and 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area.
2. ### math

a farmer has enough fencing to build 40 feet of fence. He wishes to build a rectangular pen nest to his barn wall forming one side of the pen. What dimension should he make the pen so as to enclose the greatest possibility area?
3. ### algebra

Ian wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Ian has 450 feet of fencing, what dimensions would maximize the area of …
4. ### math

Farmer Hodges has 50 feet of fencing to make a rectangular hog pen beside a very large barn. He needs to fence only three sides because the barn will form the fourth side. Studies have shown that under those conditions the side parallel …
5. ### Geometry

A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen?
6. ### calculus optimization problem

A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the pen …
7. ### calculus

a farmer wants to make a rectangular pen from 200 feet of fencing. he plans to use a 100 foot wall along with some of the fencing to make one side of the pen. find the dimensions of the pen that will make the enclosed area as large …
8. ### Math

Manuel wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Manuel has 750 feet of fencing, what dimensions would maximize the …
9. ### algebra

A farmer has 25 yards of fencing to make a pig pen. He is going to use the side of the barn as one of the sides of the fence, so he only needs to fence 3 sides. What should be the dimensions of the fence in order to maximize the area?
10. ### math

Trent wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Trent has 400 feet of fencing, what dimensions would maximize the area …

More Similar Questions