3-4 Linear Programming
(p. 139)
Algebra 2
Prentice Hall, 2007
Objectives
You will…
Model a real-world situation using the
LINEAR PROGRAMMING technique.
Create a FEASIBLE REGION on a
coordinate plane given 3 or more
CONSTRAINTS.
Recognize and find the MAXIMUM and
MINIMUM values of a feasible region.
Definition
Linear Programming is a technique
used to determine the maximum or
minimum value of some quantity based
on an objective function.
Process
1. Write inequalities given a list of constraints
or restrictions.
2. Graph the inequalities on the same
coordinate plane.
3. Locate the coordinates of the vertices of the
feasible region.
4. Substitute the values of each vertex point
into the objective function to see which
produces the highest (max) or lowest (min)
value.
Example
Suppose you want to buy some tapes and CDs.
You can afford as many as 10 tapes or 7 CDs. You
want at least 4 CDs and at least10 hours of
recorded music. Each tape holds about 45 minutes
of music, and each CD holds about an hour.
The “object” is to spend the least amount possible
and still get what you want. If tapes cost $8 and
CDs cost $12, the objective function is
C  8x  12y
Example (contin.)
Step 1: Write inequalities based on the
constraints. (Define your variables 1st!)
• Can afford 10 tapes…
or 7 CD’s…
• Want at least 4 CD’s…
• Want 10 hours of music, knowing that
tapes holds 45 min & CD’s hold 1 hour…
Example (contin.)
Step 2: Graph your inequalities.
12
10
8
6
4
2
-5
5
-2
-4
10
Example (contin.)
Step 3: Determine the coordinates of the
feasible region.
12
10
8
6
4
2
-5
5
-2
-4
10
Example (contin.)
Step 4: Which vertices meet the
objective function?
What IS the objective function?
– Well, if the object is to spend the least
amount of money and tapes cost $8
while CD’s cost $12, you want to
“minimize” the function C  8x  12y
– So, test all the vertex points to see
which one results in the lowest C value.

Assignment
3-4 p. 142: 2, 6, 7, 16, 18, 20
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