AP Calc BC - Aim #30 - optimization completed.notebook
November 10, 2015
Unit 3 -
The newly acclaimed "Matrix" restaurant in NYC is designing a
base. The box is to be built from a piece of cardboard 25 cm wide
and 40 cm long by cutting out a square from each corner and then
bending up the sides. Write an equation for the volume of the
container.
Sep 4-8:29 PM
What is the domain
maximize
x=5
May 23-7:09 PM
1
AP Calc BC - Aim #30 - optimization completed.notebook
November 10, 2015
A soccer field located next to a school building will be fenced in.
No fence will be required on the side lying along the building. The new
wood fence costs $12 per meter for the side parallel to the building,
soccer field that will maximize the area on a budget of $3600.
Maximize:
Constraint:
225 m x 150 m
May 23-7:05 PM
A juice can in the shape of a right circular cylinder is to have the
volume of 1 liter (1000 cm3). Find the height and radius that minimize
the surface area of the can - and thus the amount of material used in
its construction.
Maximize:
Constraint:
May 23-7:05 PM
2
AP Calc BC - Aim #30 - optimization completed.notebook
November 10, 2015
We want to construct a box whose base length is 3 times the base
width. The material used to construct the top and the bottom is $10/
ft2 and the material to build the sides cost $6/ft2. If the box must
have a volume of 50 ft3, determine the dimensions that will minimize
the cost to build the box.
Minimize:
Constraint:
1.8821 x 5.6463
May 23-7:05 PM
A Norman window is being built such that the bottom is a
rectangle and the top is a semi-circle. If there are 12 meters of
framing material available, what are the dimensions of the window
that will let in the most light?
Maximize:
Constraint:
May 23-7:05 PM
3
AP Calc BC - Aim #30 - optimization completed.notebook
November 10, 2015
Determine the point(s) on the graph of y = x2 + 1 that are closest
to the point (0, 2).
Minimize:
Constraint:
May 23-7:05 PM
that will maximize the crop.
Maximize:
18 trees
May 23-7:05 PM
4
AP Calc BC - Aim #30 - optimization completed.notebook
November 10, 2015
Wrap it Up! A trough for holding water is formed by taking a piece of
sheet metal 60 cm wide and folding up the 20 cm on either end as
shown below. Determine the angle θ that will maximize the amount of
water the trough can hold.
Maximize:
[hint - think two triangles and one rectangle to maximize the cross section!]
May 23-7:05 PM
Homework: Homework #30 - pp 230-233: 3, 6, 11, 18, 20, 27, 30
A
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May 26-8:18 PM
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