College Algebra
posted by Madeline .
A farmer needs to build a rectangular corral for his animals. He has 200 yards of fencing available. He needs to make 4 pens. What is the largest corral he can create? (Remember the pens also count as a part of the perimeter, not just the outside of the corral)

depends on the configuration of the pens. A longs skinny corral with 4 pens in a row? Or a rectangular corral with a 2x2 arrangement of pens?
If the first, then we have two lengths and 5 widths.
2x+5y = 200
area = xy = x(2002x)/5 = 2/5 x^2 + 40x
the vertex of the parabola is at x=40/(4/5) = 50
So, the corral is 50 by 25
If the pens are in a grid, then we have 2 length and 3 widths:
2x+3y = 200
area = xy = x(2002x)/3 = 2/3 x^2 + 200/3 x
The vertex is now at x=50, so the corral is 50 by 33.33
Looks like the squareish pen is bigger. 
write the equation for the line that passes through the point (4,7) and is perpendicular to 3y8=x4. leave equation in thw pointslope form show all work
Respond to this Question
Similar Questions

College Algebra
A farmer has 100 yeards of fencing with which to enclose two adjacent rectangular pens both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens together (a rectangle) … 
Algebra  Math
A farmer has 100 yards of fencing with which to enclose two adjacent rectangular pens  both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens Together (rectangle … 
Algebra 2
A farmer has 120 ft. of fencing available to enclose 2 adjacent rectangular pens alongside his barn. NO fencing is required along the bard side. He needs to have a total of 930 sq.ft. Determine the width (x) and the combined length … 
cal
a rancher has 4000 feet of fencing for constructing a rectangular corral. one side of the corral will be formed by a barn and requires no fence. three exterior fences and 2 interior fences partition the corral into 3 rectangular regions. … 
area and perimet
Farmer Brown has 700 yards of fencing with which to build a rectangular corral divided into two pens. He builds a corral that uses the river as one side so he only has to fence the other 3 sides and the divider down the middle 
College Algebra
A rancher needs to build four identical pens for his animals as shown in the diagram below. He has 240 feet of fencing. He does not need to put the fence along the barn. Find the length and width that would maximize the area of the … 
algebra
A pet boarding facility wants to build two adjacent pens of equal size. They are using the length of the dog kennel as one side of the two pens. They have 324 feet of fencing to build the pens. What width should he make the pens to … 
Algebra
Word Problems: 1. A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. If he needs no fence along the river, what are the dimensions of the field that he can fence with the largest … 
math
An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total … 
Math
A farmer has 400 feet of fencing with which to build a rectangular corral having two internal dividers both parallel to two of the sides of the corral. What is the maximum total area of such a corral?