Question

Consider the following problem: A farmer with 650 ft of fencing wants to enclose a rectangular...

Consider the following problem: A farmer with 650 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

(a) Draw a diagram illustrating the general situation. Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides.

(b) Write an expression for the total area A in terms of both x and y.

A=

(c) Use the given information to write an equation that relates the variables.

(d) Write the total area as a function of one variable.

A(x) =

(e) Finish solving the problem by finding the largest area.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A rancher with 1000 feet of fencing wants to enclose a rectangular area and then divide...
A rancher with 1000 feet of fencing wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle as indicated below. If x represents the length of the common fence, find a function that models the total area of the three pens in terms of x. (Your answer will be a function or expression.)
A javalina rancher wants to enclose a rectangular area and then divide it into 6 pens...
A javalina rancher wants to enclose a rectangular area and then divide it into 6 pens with fencing parallel to one side of the rectangle. There are 660 feet of fencing available to complete the job. What is the largest possible total area of the 6 pens?
A farmer wants to fence in and area of 1.5 million square feet in a rectangular...
A farmer wants to fence in and area of 1.5 million square feet in a rectangular field. He then divides the area in half by putting another line of fencing parallel to one of the sides of the rectangle in the interior of the area. What is the dimensions of the rectanglular area that minimizes the amount of fencing used. Let x denote the length of fencing (in million of ft) along the direction where 3 pieces of fencing is...
A farmer is building a fence to enclose a rectangular area against an existing wall, shown...
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 184 feet of fencing, what is the largest area the farmer can enclose?
A farmer wants to enclose a rectangular field by a fence and divide it into 2...
A farmer wants to enclose a rectangular field by a fence and divide it into 2 smaller but equal rectangular fields by constructing another fence parallel to one side. He has 6,000 yards of fencing.(a) draw picture (b) Find the dimensions of the field so that the total area is a maximum. (c)  Find the dimensions of the rectangular field the farmer can make the will contain the largest area.
A farmer has 420 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a...
A farmer has 420 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a common side. What dimensions should be used for each pig pen so that the enclosed area will be a maximum? The two adjacent pens have the same dimensions. Find the absolute maximum value of f(x)= x4−2x
A farmer has 800 ft of fencing, and wants to fence off a rectangular field that...
A farmer has 800 ft of fencing, and wants to fence off a rectangular field that borders a river with a straight bank. She needs no fence along the river. What are the dimensions of the field of largest area?
A campground owner has 1900 m of fencing. He wants to enclose a rectangular field bordering...
A campground owner has 1900 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. Let x represent the width of the field. a)Write an expression for the length of the field. b)Find the area of the field (area=length x width) c)Find the value of x leading to the maximum area. d)Find the maximum area.
A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs...
A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides. Find the cost of the least expensive fence. The cost of the least expensive fence is $_
1. A rectangular pen is built with one side against a barn. If 600 m of...
1. A rectangular pen is built with one side against a barn. If 600 m of fencing are used for the other three sides of the pen, complete the following to find the dimensions that maximize the area of the pen. True or False: the objective function is the perimeter function, P=2x+y 2. Let A be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT