intermediate algebra
posted by irma on .
A farmer with 3000 feet wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

Let x be the side length parallel to the highway. The side lengths perpendicular to the highway must be
(1/2) (3000 x)
The area is
A = (x/2)*(3000x) = 3000x x^2/2
When there is a maximum,
dA/dx = 0 = 3000  2x
x = 1500 feet
I used calculus but you can try completeing the square or try various values of x until you get a maximum area.
The enclosed area will be 1500 x 750 = 1,125,000 ft^2 
where did you get the 750? I have a similar problem here:
a farmer wants to build a rectangular pen using a side of a barn and 60ft of fence. find the dimensions and area of the largest such pen 
Let l = measure of the parallel side of the highway in meters
w = measure of the perpendicular side of the highway in meters
l + w = 3000
l = 3000  w
length = 3000  w
width = w
A= lw
**since we will only use 1 side of the length, we will use:
A= [(3000w)/2]w 0r w[(3000w)/2]
= (w^2)/2 + 1500w
**complete the square
= 1/2 (w^2  3000w + 225,000) + 1,125,000
= 1/2 (w1500)^2 + 1,125,000
w=1500
A max.= 1,125,000
**substitution
l=(3000w)/2
=(30001500)/2
=750
dimensions: 1500 x 750