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

Let x = length
Let y = width
From this we know that area A=xy.

Answer 2

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.

Answer 3

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

Answer 4

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)

Answer 5

Happy Math

Answer 6

Did you follow with understanding?

Answer 7

yes, thank you :)

Answer 8

Great, have a nice day :)