Question

A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Find the dimensions of the rectangle he should use to minimize the cost of fencing. List the dimensions in non-decreasing order.

Answer 1

http://openstudy.com/users/chlorophyll#/updates/50b95e40e4b0c789d510669d

Answer 2

would it be 3,000 and 2,000?

Answer 3

I might have inputed the answers differently. I'll try again, thank you!

Answer 4

If you want me to double check your work out solution, I'll be happy, but don't ask me for the answer, I myself haven't computed it yet!

Answer 5

Here's what I did:
2p + 3q

LW = 6 x 10^6 sqft.
=>2p + [3(6x10^6)
=2p + (18 x 10^6) (p^-1)
dP/dp = 2+ (18 x 10^6)(-1)(p^-1)
=> 2 + [(18 x 10^6)/(p^2)] = 0
2p^2 - 18 x 10^6 = 0
p^2 = sqrt 36 and sqrt 10^6
= 6 x 1,000

THUS, p= 6,000ft
q = (6 x 10^6)/ 6,000 = 1,000 ft

Not sure if this is correct.

Answer 6

I got w = 2,000 ft and L = 3,000 ft

Answer 7

the other way was:
3x +2y
A =xy = 6,000,000
y = 6,000, 000/x
L = 2x + 12,000,000/x
3- (12,000,000/x^2) = 0
3 = 12, 000,000/x^2
sqrt x^2 = sqrt 4,000,000
x = 2,000 and y = 3,000
What's non-decreasing order?

2000ft, 3000ft?

Answer 8

so i guess that was the correct way. AWW, cute!

Answer 9

Okay, I got it. Thank you so much!

Answer 10

your way is the best way and probably the easiest. thank you! :)

Answer 11

Now I'm happy! You're the first one compliment my way is the easiest one ;)

Answer 12

:) It helped me get the correct answer, so I'm pretty excited. I was on my last try as well!