A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
anonymous
 5 years ago
A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Area = LW Perimeter = L1 + L2 + 2W 180 = LW 2L(5) + W(5) + L(15) = cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0since 180 = LW, we can say that W = 180/L

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that L(15) up there should be W(15) 2L(5) + (180/L)(5) + (180/L)(15) = Cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010L +900/L + 2700/L = cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0maybe we need to minimise the perimeter :) P = 2L + 2W P = 2L + 2(180/L) P = 2L + 360/L P = 2L^2 + 360  take the derivative L

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0dP = L(2L)  (2L^2+360)(1)  L(L)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04L^2  2L^2  360 2L^2360  =  L^2 L^2 I adjusted for my stupidity :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when the top is 0 we got a min or a max

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry just a little confused because it 280 but it still works i can just go back and plug in my numbers

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02(L^2 180) = 0 L^2  180 = 0 L^2 = 180 L = +sqrt(180)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0...... lol ..........

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i forgot to adjust for all my stupidity lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it ok you have it i see just a mix up of numbers is all...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0W = 280/sqrt(280) W = sqrt(280) as well, so its a square I guess...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Well, that would maximise the area ..... but it doesnt help with costs :) lets see what costs gets us

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02L(5) + (280/L)(5) + (280/L)(15) = Cost 10L + 900/L + 4200/L = cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010L^2 + 900 + 4200  = cost L

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0stop me when I get lost :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010L^2 + 5100  = cost L L(20L)  1(10L^2 + 5100)  = cost' L^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait i am confused....it wants to know the dimensions...so why are we looking for cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.020L^2 10L^2 5100 = 0 10L^2  5100 = 0 10(L^2 510) = 0 L^2  510 = 0 L=sqrt(510) because..... the diminsions dont need to be "minimized for area, they need to be minimized for cost...makes sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets plug sqrt(510) into the calulator to give us a roundabout: 22.58 is what I get for one side :) 280 = LW 280 = 22.58W 280/22.58 = W 12.40 = W

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Now figure out how much we need for the most expensive side :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02(22.58)(5) + 12.40(5) + 12.40(15) =? 2(12.40)(5) + 22.58(5) + 22.58(15)? which is cheaper?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my answer are not correct....thats what my website i have to submit my answer into is telling me...so i don't know if there was a mix up somewhere

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0maybe..... I could of thought it wrong as well. but to me, to minimize cost, we would derive the equation for Price and not Area, figure out what a side would be for that price then figure the rest out...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0280/L or 280/W doesnt matter, since its just a name for a side..right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0polpak is here.... hell know what I did wrong ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, we have \[Area = LW = 280 \rightarrow W = 280/L\] \[Cost = 5(L + 2W) + 15L \] \[\rightarrow Cost = 20L + (5*2)(280)/L \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks figured it out...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dL}Cost = 20  \frac{2800}{L^2}\] The cost is a min when the derivative is 0 \[\rightarrow 0 = 20\frac{2800}{L^2}\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so where did I miss it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't tell, but you have a lot of cost functions and none of them look the same as the one I have.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0:) they are similar.... I was just going over that to see if I made a mistake

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I did 2L(5) + 180(5)/L + 280(15)/L for cost... but that should be correct either way....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0make that 280 up there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If those are both 280 instead of 180 it should be ok.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It just means that your L is my W.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010L +900/L + 4200/L = cost

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok then you would have \[Cost' = 10 900/L^2  4200/L^2\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0right... you derived them seperately which is fine :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010L^2  5100 = 0 L^2  510 = 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0L=sqrt(510).... is it right? the same as yours?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you get L = sqrt(140)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But my L is your W remember.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm....... maybe thats right, havent checked that out yet :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.011.83 = you 12.40 = me.....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hrm. Lemme check that cost again.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0280*5 = 1400 ... not 900

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sqrt(560).... might be better :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Yep... thats it.... I just forgot how to multiply integers LOL

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thats why I always save the plugging the numbers part for last.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or as late as I can without making it look horrible.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah.... itda helped if I started out with the 280 and worked it, but..... you know :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.