Homework Help: Algebra

Posted by ShelbyA on Sunday, April 29, 2012 at 7:59am.

a farmer wants to enclose a rectangle garden using the sides of her barn as one side of the rectangle. what is the maximum area which she can enclose with 60ft of fence? what should the dimensions of the garden be to give this area?

Max area which she can enclose with 60ft of fence in sq.ft?

dimensions to give area is 30ft by___ft?

Algebra - Damon, Sunday, April 29, 2012 at 8:06am
2 w + L = 60 so L =60-2w
A = w L
A = w (60-2w)
A = -2w^2+60 w

2 w^2 -60 w = -A
w^2 - 30 w = -A/2
w^2 - 30 w + 225 = -A/2 + 450/2
(w-15)^2 =-(1/2)(A-450)
w = 15
L = 60-30 = 30
A = 450
Algebra - Damon, Sunday, April 29, 2012 at 9:06am
If you know any calculus, you can do this much faster
A = -2w^2+60 w

dA/dw = 0 at extreme = -4 w + 60
so w = 60/4 = 15 at max

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