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?

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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?

Mathematics
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Let x = length Let y = width From this we know that area A=xy.
We also know that perimeter is P=2x+2y we also know that 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.
We now substitute this value in the area equation A=xy. A=(1000-4y/6)y \[A=1000y-4y ^{2}/6=1000y-2y ^{2}/3\] differentiate and set to equal zero (0) \[1000-(-4y/3)=0 \] Solve for y and obtain y=750ft

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Then solve for x, getting x=500. the cost then becomes $3000 for the x sides (2*500*$3.000) and $3000 for the two y sides (2*750*$2.00)
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