Question

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?

Answer 1

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