Suppose that a rectangular area is to be fenced, except one side must be fenced twice because it runs along a river. If the amount of fencing is 320 yards in length, what is the maximum area that can be fenced?
I see this question answered below, but We need to maximize the area, which is xy.
From the perimeter, y = 160-3/2x
so, area = xy = 160x - 3/2(x^2) - why is this x squared? and once you derive the ax^2+bx+c=0 formula, how do you maximize the area?

Question

Suppose that a rectangular area is to be fenced, except one side must be fenced twice because it runs along a river.  If the amount of fencing is 320 yards in length, what is the maximum area that can be fenced?
I see this question answered below, but We need to maximize the area, which is xy.
From the perimeter, y = 160-3/2x
so, area = xy = 160x - 3/2(x^2) - why is this x squared? and once you derive the ax^2+bx+c=0 formula, how do you maximize the area?

anonymous · Answer

P=3L+2W=320
3L=320-2W
L=320/3-2W/3

anonymous · Answer

my professor has it as P=2L+3W=320, and still comes up the same L=320/3-2/3w - which obviously if you solve for L, it yields a different answer.  Is the end outcome the same regardless of what side of the fence you assign the double fencing to?? The problem does not specify what side they are adding the double fence to.

anonymous · Answer

Yes, you are right it doesn't really matter which side to double. I did it because of your second posting.

anonymous · Answer

if L=320/3-2W/3, then for arae you will multiply L*W
L*W=(320/3-2W/3)*W=320W/3-2W^2/3

anonymous · Answer

This quadratic equation with negative first coefficient. For max you need to find coordinates of a vertex (-b/2a, f(-b/2a)). First coordinate is width, the second is max area. Can you do the rest by yourself?

anonymous · Answer

I think so. thanks for your help

anonymous · Answer

You are welcome. Hope it helps.

anonymous · Answer

L=320/3-2w/3, how does this equal 320-160/3?

anonymous · Answer

it doesn't

anonymous · Answer

attachment

anonymous · Answer

this is the answer key my professor gave me if u have a sec to look.  I do not understand I guess.. maybe I am just dumb.

anonymous · Answer

mid term is in 7 hours. 2nd one this week...

anonymous · Answer

your professor gave you very good and detailed answers. I would say much better that I was telling you. Can you tell me where you get lost?

anonymous · Answer

The length of L=320/3-2w/3 =320-160/3 - i dont understand where she gets the 160

anonymous · Answer

we were talking about vertex. -b/2a=80. THis is value of W. Then she plug it into formula, replacing W with value 80, she gets 160/3

anonymous · Answer

ahh perfect.  thank you again, that sums it up for me
!!

anonymous · Answer

I am glad that I helped. If you have chance, print out answers and try to do your test one more time tomorrow. If you get confused, you can look at detailed explanation. Of course if you will have time! Good luck on your midterm!