# 3-7: Optimization Problems ```3-7: Optimization Problems
Objective:
1. To solve applied
maximum and
minimum problems
Assignment:
• P. 223-227: 1, 9, 11, 13,
18, 19, 21, 23, 24, 27,
44, 56, 57
You will be able to solve
applied maximum and
minimum problems
The Bigger Box
As employees of Lee J.
Monroe, we have been
box with maximum
volume.
The Bigger Box
To make said box, we will
take a sturdy sheet of
cardstock, which
measures 8.5 inches by 11
inches, and cut a square
from each corner, keeping
in mind that the box must
be as voluminous as
possible, and then make a
box from the resulting net.
Optimization Algorithm
Identify all given quantities and quantities
to be determined, and sketch a picture.
Step 1
Write a primary equation for the
quantity to be optimized.
Step 3
Step 2
Reduce the primary equation to one
having a single independent variable
using secondary equations.
Optimization Algorithm
Step 4
Determine a feasible domain for the
primary equation.
Closed Interval Test
Use calculus to determine the
minimum or maximum value.
First Derivative Test
Step 5
Second Derivative Test
Exercise 1
A manufacturer wants
to design an open box
having a square base
and a surface area of
108 square inches.
What dimensions will
produce a box with
maximum volume?
Exercise 2
Which points on the
graph of 𝑦 = 4 − 𝑥 2
are closest to the
point (0,2)?
Exercise 3
A rectangular page is to contain 24 square
inches of print. The margins at the top and
bottom of the page are to be 1 &frac12; inches, and
the margins on the left and right are to be 1
inch. What should the dimensions of the
page be so that the least amount of paper is
used?
Exercise 4
Two posts, one 12 feet high and the other 28
feet high, stand 30 feet apart. They are to be
stayed by two wires, attached to a single
stake, running for ground level to the top of
each post. Where should the stake be
placed to use the least amount of wire?
Exercise 5
Four feet of wire is to be
used to form a square
and a circle. How much
of the wire should be
used for the square and
how much should be
used for the circle to
enclose the maximum
total area?
3-7: Optimization Problems
Objective:
1. To solve applied
maximum and
minimum problems
Assignment:
• P. 223-227: 1, 9, 11, 13,
18, 19, 21, 23, 24, 27,
44, 56, 57
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