Math
posted by booyah on .
A rectangular dog pen is to be constructed using a barn wall as one side and 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area.

20 x 20

let the length be y m (the single side)
let the width be x m
so we know that 2x + y = 60
or y = 60  2x
Area = xy
= x(602x)
= 2x^2 + 60x
At this point I don't if you know Calculus or not.
If you do, then
d(Area)/dx = 4x + 60
= 0 for a max of area
4x + 60 = 0
x = 15
then y = 30
if you don't take Calculus, we have to complete the square
area = 2(x^2  30x)
= 2(x^2  30x + 225  225)
= 2((x15)^2  225)
= 2(x15)^2 + 450
so the area is a maximum when x = 15
and then y = 6030 = 30
by either method,
the width has to be 15 m, and the length has to be 30 m for a maximum area of 15(30) or 450 m^2
(LULU's answer only gives an area of 400 )