1) A two-pen corral is to be built. The outline of the corral forms two identical adjoining rectangles. If there is a 120 ft. of fencing available, what dimensions of the corral will maximize the enclosed area?

Question

1)	 A two-pen corral is to be built.  The outline of the corral forms two identical adjoining rectangles.  If there is a 120 ft. of fencing available, what dimensions of the corral will maximize the enclosed area?

anonymous · Answer

@electrokid  can u help? @Mertsj

anonymous · Answer

if the dimensions of one pen are x by y, then the area is xy, y is the dimension in common.
area of both 
A = 2xy
perimeter = 120 = 4x+3y

combine the two equations to get A as a function of x or y
120 = 4x+3y
4x = 120–3y
x = 30 –(3/4)y
A = y(30 –(3/4)y)= 30y –(3/4)y²

differentiate and set equal to 0 to get max/min
A' = 30 – (3/4)2y = 0
(3/2)y = 30
y = 20

x = 30 –(3/4)y = 30 –(3/4)20 = 15

pens are 20 x 15, and overall is 30 x 20

anonymous · Answer

huh?

mertsj · Answer

The solution provided is exactly right.  What class are you taking that you have no understanding of the solution?

anonymous · Answer

Noi thought he would explain it but okay