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?

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-4 y2 / 6=1000y-2 y2 / 3 differentiate and set to equal zero (0) 1000 - (-4y/3) = 0 Solve for y and obtain y=750ft