Question

un has 1200 feet of fencing materials to build a pen for his sheep and goats. The pen will be a rectangle with a divider down the middle. What should be the maximum are for the pen?

Answer 1

the fence perimeter = 1200
let the length be 'x' and breadth be 'y'
so, 2(x+y) =1200
y= 600-x
now Area =A=xy =x(600-x)
to get max. area, differentiate A and set it =0

Answer 2

A = 600x -x^2
since you can take simple derivates, can you derivate A ?

Answer 3

600-2x

Answer 4

is it right?

Answer 5

now set that =0 and find x

Answer 6

yes, thats correct ! good :)

Answer 7

now set that =0 and find x

Answer 8

300

Answer 9

yes, now Area = x(600-x) =... ?

Answer 10

90000

Answer 11

\(\checkmark
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Answer 12

is that the answer already?

Answer 13

yes, you needed max area...dimensions we found by differentiating, and then we plugged it into area and got 90000 sq. ft.