SOLUTION: You want to form a rectangular pen of area a = 70 square feet. (See the figure below.) One side of the pen is to be formed by an existing building and the other three sides by a fe

Question 1146109: You want to form a rectangular pen of area a = 70 square feet. (See the figure below.) 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 length, in feet, of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is 70/w, so the total amount F = F(w), in feet, of fence required is the rational function
F = 2w +
70
w
.
Determine the dimensions of the rectangle that requires a minimum amount of fence. (Round your answers to two decimal places.)
width
ft
length
ft

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The function for the length of fence is

Find the value of x that minimizes the area by finding where the derivative is zero.

The width that minimizes the total amount of fence required is feet.

That makes the length

Note that, to minimize the total length of fence required, the length is twice the width. That is always the case, regardless of what the total area is.

So if you are in a position where you see this kind of problem often -- e.g. you are on a high school math team -- then you can just memorize this fact.

Then to solve this problem without doing the calculus, you just solve

leading very quickly to dimensions of and .
RELATED QUESTIONS
You want to form a rectangular pen of area, a=70 ft^2. One side of the pen is to be... (answered by solver91311,richard1234)

you used 75 yards of fencin to make a rectangular pen. if one side of the pen is 18 yards (answered by ewatrrr)

Please help me answer: You have 120 feet of fencing to make a pen for your dog. You... (answered by mananth)

300 ft of fencing is available to fence a rectangular pen where one side will be ordered... (answered by rfer)

A farmer plans to build a fence around a rectangular pen that is 16 feet long. The area... (answered by checkley77)

A farmer plans to build a rectangular pen taht is 16 feet long. The area of the pen is 80 (answered by edjones,Edwin McCravy)

Can you give me detailed steps on how to set up and solve? Scott wants to build a... (answered by josgarithmetic)

please help me find solution to this problem. Good day and thank you! Troy made a... (answered by Alan3354)

I need help with solving this problem. Here is the question: Chris has purchased 50 feet... (answered by lwsshak3)