Posted by booyah on Saturday, December 18, 2010 at 7:16pm.
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.

Math  LULU, Saturday, December 18, 2010 at 8:00pm
20 x 20

Math  Reiny, Saturday, December 18, 2010 at 9:49pm
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 )
Answer This Question
Related Questions
 algebra  Ian wants to build a rectangular pen for his animals. One side of the ...
 math  a rectangular pen is to be constructed alongside a barn using 120 feet of...
 math  Trent wants to build a rectangular pen for his animals. One side of the ...
 Math  Manuel wants to build a rectangular pen for his animals. One side of the ...
 Geometry  A farmer wants to fence in a rectangular pen using the wall of a barn...
 calculus optimization problem  A farmer has 460 feet of fencing with which to ...
 college math  a rectangular dog pen is to be constructed so that one side is ...
 Math  You are designing a rectangular dog pen off the back of your house. The ...
 Prealjebra  a rectangular dog pen is to be constructed so that one side is ...
 Algebra  A rectangular pig pen is made of 84 meters of fencing on three sides. ...
More Related Questions