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A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides

will use heavy-duty fencing selling for $3 a foot, while the remaining two sides will use standard

fencing selling for $2 a foot. What are the dimensions of the rectangular plot of greatest area

that can be fenced in at a cost of $6000?

Verified Answer :

pkmnmushy

Ok lets do this like this:
Let x = length
Let y = width

From this we know that area A=xy.
Now, perimeter is P=2x+2y

cost would be 3(2x)+2(2y) or 6x +4y=$6,000.00.

From this cost equation we solve for x in terms of y
6x=6000-4y
x=1000-(4y)/6.
now lets substitute this value in the area equation A=xy.
A=(1000-4y/6)y
A=1000y−4y2/6=1000y−2y2/3
differentiate and set to equal zero (0)
1000−(−4y/3)=0
Solve for y and obtain y=750ft

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