Posted by awes on Tuesday, September 13, 2011 at 4:37am.
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?
- math - Damon, Tuesday, September 13, 2011 at 5:35am
length = x
width = y
area = A = x y
length of fencing = 2x+y = 40
y = 40-2x
A = x (40 - 2x)
A = 40 x - 2 x^2
maxmimum A , when dA/dx = 0
0 = 40 - 4 x
x = 10
then y = 40 - 20 = 20
area = A = 200
alternatively look at parabola
2 x^2 -40 x = -A
x^2 - 20 x = -(A/2)
x^2 - 20 x + 100 = -(A/2) + 100
(X-10)^2 = -(1/2)(A+200)
vertex at x = 10, A = 200
- math - bobpursley, Tuesday, September 13, 2011 at 5:38am
dArea/dL=0=40-2L + l(-2)
L=10 W= 20 so the pen is 10x20,with the barn serving as a 20ft side.
graph area vs L. Where is it maximum?
Answer This Question
More Related Questions
- Geometry - A farmer wants to fence in a rectangular pen using the wall of a barn...
- calculus optimization problem - A farmer has 460 feet of fencing with which to ...
- Calculus 2 - A farmer wishes to build a fence for 6 adjacent rectangular pens. ...
- algebra - Ian wants to build a rectangular pen for his animals. One side of the ...
- math - Trent wants to build a rectangular pen for his animals. One side of the ...
- math - a farmer wants to build a rectangular pen using a side of a barn and 60ft...
- math - Farmer Hodges has 50 feet of fencing to make a rectangular hog pen ...
- Pre-Calc - A farmer is making a pig pen next to the barn. He has enough ...
- Math - Manuel wants to build a rectangular pen for his animals. One side of the ...
- Calculus Follow Up - A farmer wishes to build a fence for 6 adjacent rectangular...