intermediate algebra
posted by irma .
A farmer with 3000 feet wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

intermediate algebra 
drwls
Let x be the side length parallel to the highway. The side lengths perpendicular to the highway must be
(1/2) (3000 x)
The area is
A = (x/2)*(3000x) = 3000x x^2/2
When there is a maximum,
dA/dx = 0 = 3000  2x
x = 1500 feet
I used calculus but you can try completeing the square or try various values of x until you get a maximum area.
The enclosed area will be 1500 x 750 = 1,125,000 ft^2 
intermediate algebra 
joe
where did you get the 750? I have a similar problem here:
a farmer wants to build a rectangular pen using a side of a barn and 60ft of fence. find the dimensions and area of the largest such pen 
intermediate algebra 
prince
Let l = measure of the parallel side of the highway in meters
w = measure of the perpendicular side of the highway in meters
l + w = 3000
l = 3000  w
length = 3000  w
width = w
A= lw
**since we will only use 1 side of the length, we will use:
A= [(3000w)/2]w 0r w[(3000w)/2]
= (w^2)/2 + 1500w
**complete the square
= 1/2 (w^2  3000w + 225,000) + 1,125,000
= 1/2 (w1500)^2 + 1,125,000
w=1500
A max.= 1,125,000
**substitution
l=(3000w)/2
=(30001500)/2
=750
dimensions: 1500 x 750
Respond to this Question
Similar Questions

Math
A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? 
intermediate algebra
A farmer with 3000 feet of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed? 
Algebra
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can … 
math
A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed? 
math
A rancher with 7000 yds of fencing wants to enclose a rectangular field that borders a straight highway and then wants to devide it into two plots with a fence parellel to the highway. If no fence is needed along the highway, what … 
College Algebra
You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river,find the length and width of the plot that will maximize the area. What is the largest area that can be … 
Pre calc
A farmer with 2000 meters of fencing wants to enclose a rectangular field that borders a barn. If the farner does not fence the side along the barn, what is the largest area that can be enclosed? 
algebra
Farmer Ed has 9 comma 0009,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed? 
Algebra
Farmer Ed has 9,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed? 
Math(HELP!)
A farmer has 120 feet of fencing to enclose a rectangular plot for some of his animals. One side of the area borders on a barn. a.) If the farmer does not fence the side along the barn, find the length and width of the plot that will …