For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 162 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence? north and south sides? east and west sides?

Question

anonymous · Answer

plz i need help i don't know what to do

anonymous · Answer

okay give me a sec

anonymous · Answer

thank you I'm so lost

anonymous · Answer

4 dollar per foot on east and west side. 2 dollar per foot on north and south side. the least expensive fense would be the LEAST use of east and west fence, thus, you need to MAXIMIZE fence on north and south side... Now think, what are two numbers that can multiply to 50? 1x50 2x25 5x10 Remember, we want the fence to cost as little as possible. So the larger number can be reasonably the north and south side while smaller side is the east and west. If you look at the 3 dimensions i provide, 1x50 is the best possible answer. Though not ask for... since the fence has four sides, you'd find the circumference of the 1x50 dimension. The total cost: north: 50x$2 east: 1x$4 south: 50x$2 west: 1x$4 -------------- sum is $208

anonymous · Answer

East/west side is 10 feet
North/south side is 20 feet
 to make this easier

anonymous · Answer

it says its wrong.....

anonymous · Answer

I might of did something wrong. Sorry, let me see if i can get some people.

anonymous · Answer

ok thank you!

anonymous · Answer

@aum @jhonyy9

anonymous · Answer

They will probably come eventually but, I have to go. Im sorry. Heres a medal for you. :)

anonymous · Answer

it says it is wrong 
what is wrong?

anonymous · Answer

$$xy=162, 8x+4y=C$$ you want to minimize C

anonymous · Answer

since 
$$xy=162$$ you know 
$$y=\frac{162}{x}$$

anonymous · Answer

the answer he provided me was wrong yes

anonymous · Answer

plug it in and get 
$$C(x)=8x+\frac{648}{x}$$ this is a calculus problem right?

anonymous · Answer

yes it is

anonymous · Answer

there is your function, domain is $x>0$ take the derivative, find the critical point etc

anonymous · Answer

dude please i have no idea what your talking about

anonymous · Answer

i don't know what a critical point is