Hi guys,

Question

I am really stuck with this problem, maybe somebody could help me out.

A rancher has 2100 feet of fencing with which to construct adjacent, equally sized rectangular pens as shown in the figure above. What dimensions should these pens have to maximize the enclosed area?

This is a picture that belonged to it as well.

i(DOT)imgur(DOT)com/qh13W07.jpg

x=
y=
Maximum area=

Thanks for your help!

Frank

Answer 1

I could not get the image to come up, but you will find that the maximum area is achieved when it is equally split among the widths and lengths.

So, 1050 will be divided among the vertical pieces, and 1050 will be split into horizontal pieces.

Define the 2100 as the sum of *x + *y = 2100
and define x or y in terms of the other.

Then you can express the area as a function of just x or y.

It will be a parabola, and the maximum area is at the vertex.

Answer 2

My Progress so far:

P=4x+3y=2100

A=2xy

A=2x(2100-4x/3) This way I was able to calculate x= 525/2 or 262.5 But I'm having a struggle rewriting the formula used in terms of y. Can somebody help?