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anonymous
 5 years ago
A Rancher wants to enclose 2 rectangular area near a river, one for sheep and one for cattle. There is 240 yd. of fencing available. What is the largest total area that can be enclosed.
anonymous
 5 years ago
A Rancher wants to enclose 2 rectangular area near a river, one for sheep and one for cattle. There is 240 yd. of fencing available. What is the largest total area that can be enclosed.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This seems to be an optimization problem. Does the river count as one side that doesn't need to be fenced?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes it is an optimization problem. No I don't believe the river counts as a side that doesn't need to be fenced. It just says near a river so..I don't think so.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, 2WidthCattle + 2LengthSheep + 2WidthCattle + 2 LengthSheep = 240 yards of fencing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And we know that length * width = area.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, Im following so far

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We also know that squares work the best, in terms of area.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So let's simplify our perimeter equation. If all four sides are the same for both pens (to form a square = maximum area), we can simplify the perimeter to 4lenghts + 4lenghts = 240 yards of fencing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We would do well to maximize both the squares so in the end, we can have 8lengths = 240 yards.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Can you solve the length of each side from there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Exactly, so each side is 30, which gives you an area of.? (A=Length*Width)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But I thought I had to use optimization

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And since you have two pens, the max would be 900*2 sq. yards

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Squares are the optimization.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we don't have to use the derivative or anything like that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is this right?! Are we forgetting about the fence in the middle that separates the animals

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's two separate pens.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we are double counting the 30 side where the 2 squares are joined

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or, that is what I am getting?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we should be able to get a bigger area if we share one side

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just thought we had to use the derivative of some function to get the max area

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think I solved it...if we share sides we can get a bigger area. We will need to use the derivative to solve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, that is probably right because that is what we are doing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First set up your sides as W = width. You will have 3 of these. You will also have two lengths. So you will have 2L+3W = 240. So L=1203/2 W 120  3/2w _____________     w  w  w ______________ 120  3/2w

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You with me so far? Sorry about the crappy drawing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, that was the hard part. Now I think all you have to do is find the Area function: A = L*W or A = (120  3/2W) * W = \[120W  3/2W^2 = A\] Then take the derivative: \[A \prime = 120  3W\] Now find where the derivative = 0 which will be it's maximum or minimum. \[0 = 120  3W \] From here you get the answer of W = 40. Now you can just punch it in and find the total area to b

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What do you think? It looks to be right to me but double check yourself.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea that sounds right thanks a lot!
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