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
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
