Question

Your sister wants to construct a rectangular garden with three separate areas for the two of you and your brother. She has 400 ft of fencing for the outer boundary and the separating fences. She asks you to calculate the dimensions in order to have the maximum enclosed total area.

(a) Find the total enclosed area, A(x), as a function of the width, x, and determine the x-interval over which it is to be maximized.

(b) Find the critical point of A(x).

(c) Use the second derivative test to check whether the critical point from part (b) is a local maximum.

(d) Use the zeroth derivative test to find the dimensions that maximize the area.

Answer #1

1. You are looking to spruce up your garden by making a
rectangular enclosure using a wall as one side and 160 meters of
fencing for the other three sides. You want to find the dimensions
of the rectangle so that you are maximizing the enclosed area.
(a) Draw and label a picture representing the problem
(b) Write the objective function and the constraint. (You do not
need to label which equation is which.)
(c) Write the area equation in...

You are looking to spruce up your garden by making a rectangular
enclosure using a wall as one side and 120 meters of fencing for
the other three sides. You want to find the dimensions of the
rectangle so that you are maximizing the enclosed area.
(a) Draw and label a picture representing the problem.
(b) Write the objective function and the constraint. (You do not
need to label which equation is which.)
(c) Write the area equation in terms...

2) A rectangular playground is to be fenced off and divided in
two by another fence parallel to one side of the playground. 400
feet of fencing is used. Find the dimensions of the playground that
maximize the total enclosed area. What is the maximum area?

Ben wants to build a rectangular enclosure for his animals. One
side of the pen will be against the barn, so he needs no fence on
that side. The other three sides will be enclosed with wire
fencing. If Ben has 450 feet of fencing, you can find the
dimensions that maximize the area of the enclosure.
A(W)=A(W)=
b) What width WW would maximize the area?
WW = ft
Round to nearest half foot
c) What is the maximum area?
AA...

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