SOLUTION: A farmer has $3600 to spend on fencing for three adjoining rectuangular pastures, all with the same dimensions. a local contracting company tells the farmer that they can build the

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Question 37629: A farmer has $3600 to spend on fencing for three adjoining rectuangular pastures, all with the same dimensions. a local contracting company tells the farmer that they can build the fence for $6.25/m. What is the largest total area that the farmer can have fenced for that price?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
the fields would look like 3 adjoining rectangles
with $3600 to spend and and a cost of $6.25/m, the farmer can
afford 3600/6.25 = 576 m of fence
He needs 4 north-south lengths and 2 east-west lengths (for example)
in order to enclose 3 rectangular fields
All these lengths will add up to 576 m.

The area enclosed is x times y

solve for y in the 1st equation

substitute this in equation 2

graph the equation

I'll guess the x value where the graph is a max is 144

factor out 144^2

The way to test this is to increase 144 a little, test it in the equation
then decrease 144 a little and test it in the equation

since the area is a little bit less than 10368 on either side
of x = 144, then this is the max.
The largest Area that can be enclosed is 10368
----------------------------
check
If x = 144, find y
xy = 10368
y = 10368/144
y = 72

OK