SOLUTION: You want to form a rectangular pen of area, a=70 ft^2. One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the width of the si

Question 597839: You want to form a rectangular pen of area, a=70 ft^2. One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the width of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is L=70/w. The total amount of fence required is the function F=2w + 70/w, in feet.
Determine the dimensions of the rectangle that requires a minimum amount of fence. Round to decimal places.
width = feet
length = feet
I have been having difficulty with area problems. Any help would be greatly appreciated. Thanks!!!
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I hope you are taking Calculus, because that is the only way I know how to solve this one.

Minimize

Take the first derivative:

Set the first derivative equal to zero and solve for the value of the independent variable at a local extremum.

Discard the negative root; measurements of distance less than zero are absurd in this context.

Take the second derivative:

Which is positive for all positive values of the independent variable. Therefore the local extreme is a minimum.

Hence the minimum amount of fence is required when the width measures . You should be able to determine the length yourself using . Using the calculator and rounding is also up to you.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Using calculus is one way to solve the problem, and is probably the most common way. It is also possible to solve this one without calculus.

If you know the AM-GM (arithmetic mean-geometric mean) inequality, you can say that

By AM-GM, equality occurs if and only if .
RELATED QUESTIONS
You want to form a rectangular pen of area a = 70 square feet. (See the figure below.)... (answered by greenestamps)
A rancher is building a pen using 150 feet of fencing. The pen will be enclosed on 3... (answered by JThomson,ikleyn)
300 ft of fencing is available to fence a rectangular pen where one side will be ordered... (answered by rfer)
I have been struggling to figure out this math problem and I was wondering if someone... (answered by scott8148)
A pen is to be formed by enclosing a rectangular fenced area in an open field. The pen... (answered by ikleyn)
you used 75 yards of fencin to make a rectangular pen. if one side of the pen is 18 yards (answered by ewatrrr)
a) A rectangular pen is build with one side against a barn. If 2100 m of fencing are used (answered by josmiceli,KMST,ikleyn)
A farmer plans to use 21 meters of fencing to enclose a rectangular pen having an area of (answered by Alan3354)
Tom is building a rectangular dog pen that we wants to enclose. The width of the pen is 2 (answered by josmiceli)