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
= -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((x-15)^2 - 225)
= -2(x-15)^2 + 450
so the area is a maximum when x = 15
and then y = 60-30 = 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 )
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