Fall 2011
Math 141 Exam 2 Topics
courtesy: Kendra Kilmer
(covering Sections 3.13.3, 6.16.4, and 7.1)
Section 3.1
•
To graph a system of linear inequalities:
•
Solve all inequalities for
y
.
•
Graph the corresponding equations. If the inequal
ity is a strict inequality (
<
or
>
) draw the line as a
dotted line to represent that the points on the line
are NOT part of the solution. If the inequaility is
inclusive (
≤
or
≥
) draw the line as a solid line to
represent that the points on the line are part of the
solution.
•
Determine which halfplane satisﬁes the inequality.
You can do this by using a test point or by using
the following “rules”. Please note that these “rules”
only work once we have the inequality solved for
y
:
•
If you have
y
≤
f
(
x
) or
y < f
(
x
) the solution
set lies below the line.
•
If you have
y
≥
f
(
x
) or
y > f
(
x
) the solution
set lies above the line.
•
Our
solution set (feasible region)
consists of all
points that satisfy all of the inequalities.
•
A solution set is
bounded
if all of the points in our
solution set can be enclosed by a circle. Otherwise, we
say that the solution set is
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 Fall '08
 JillZarestky
 Set Theory, Equations, Inequalities, Optimization, objective function, linear programming problem

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