Advance Organizer

Chapter 3 Linear Programs
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Section 3.1 Linear Inequalities in Two Variables
Section 3.2 Solutions of Systems of Inequalities:
A Geometric Picture
Section 3.3 Linear Programming: A Geometric Ap
proach
Section 3.4 Applications


Graph the linear inequality.


Graph the linear inequality.


Graph the linear inequality.


Graph the linear inequality.


Section 3.1

Graphing a Linear Inequality
1. Graph the inequality of the form ax + by < c.
(The procedure also applies if the inequality symbols

are <, > or >.)
2. Select a point that is not on the line from one half
plane. The point (0,0) is usually a good choice when it
is not on the line. If (0,0) is on the line. If (0,0) is on
the line, use a point that is not on the line.
Continued on next slide


Continued
3. Substitute the coordinates of the point for x and y in the
inequality.
a) If the selected point satisfies the inequality, then shade
the half plane where the point lies. These points are on
the graph.
b) If the selected point does not satisfy the inequality, shade
the half plane opposite the point.
c) If the inequality symbol is < or >, use a dotted line for
the graph of ax + by = c. This indicates that the points
on the line are not a part of the graph.
d) If the inequality symbol is < or >, use a solid line for the
graph of ax + by = c. This indicates that the line is a part
of the graph.


Example
An automobile assembly plant has an assembly line that
produces the Hatchback Special and the Sportster. Each
Hatchback requires 2.5 hours of assembly line time, and each
Sportster requires 3.5 hours. The assembly line has a maximum
operating time of 140 hours per week. Graph the number of cars

of each type that can be produced in one week.



A bakery is making whole-wheat bread and apple bran muffins. The
bread takes 4 hours to prepare. The muffins take 0.5 hour to prepare. The
maximum preparation time available is 16 hours. Graph the number of of
each type that can be prepared in one day.


Acme Manufacturing has two product lines. Line A can produce 200
gadgets per hour and line B can produce 350 widgets per hour. Because
of warehouse limitations, the total number of gadgets and widgets
produced must not exceed 75,000. Write an inequality that describes the
number of each that can produced and graph it.


A service club agrees to donate at least 500 hours of community service.
A full member is to give 4 hours and a pledge is to give 6 hours. Write
an inequality that expresses this information and graph it.


On a typical long distance call you talk for 30 minutes. On a typical local
call you talk for 10 minutes. Your phone company offers a special low
rate of $0.08 per minute for long distance calls and $0.03 per minute for
local calls, for customers who spend at least 240 minutes on the phone
per month. Your parents have set a limit of no more than 15 long
distance calls per month and 30 local calls per month. Write some
inequalities that describe this situation.

Two manufacturing plants make the same kind of bicycle. The table
gives the hours of general labor, machine time, and technical labor
required to make one bicycle in each plant. For the two plants combined,
the manufacturer can afford to use up to 4000 hours of general labor, up
to 1500 hours of machine time, and up to 2300 hours of technical labor
per week. Write some linear inequalities that describe this situation.


HW 3.1
Pg 202-204 1-35


3.2 Systems of Linear
Inequalities


Graph the system of linear inequalities.


Graph the system of linear inequalities.


Graph the system of linear inequalities.


Graph the system of linear inequalities.


Graph the system of linear inequalities.

Graph the system of linear inequalities.


Graph the system of linear inequalities.


Graph the system of linear inequalities.


Your Turn
Graph the system of linear inequalities.