Slide 1
Simplex Method
Finite Math
Section 5.1
Slide 2
Standard Maximization
Problems
A linear programming problem is a
standard
maximization problem
if the following
conditions are met:
The objective function is linear and is to be
maximized.
The variables are all nonnegative
(i.e., x
≥
0, y
≥
0, z
≥
0, …).
The structural constraints are all of the
form ax + by + …
≤
c, where c
≥
0.
Slide 3
Examples
The following constraints are in the form
appropriate for a standard maximization
problem:
2x – 3y
≤
9
–5x + 2y
≤
11
x + 5y + 2z
≤
8
The following constraints are
not
in the
form appropriate for a standard maximization
problem:
x + 4y
≥
3
2x + y
≤
- 4
–2x + 3z
≥
y + 11
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Slide 4
Slack Variables
The first step in the simplex method is to
convert each structural constraint into an
equality by adding a
slack variable
to
the left side and replacing the inequality
symbol with an equal sign.
Slide 5
Slack Variables
Each constraint requires a different slack variable.
A slack variable “takes up the slack” of the inequality
and ensures equality.
For any point in the feasible region of a standard
maximization problem, the value of each slack
variable is nonnegative.

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- Spring '08
- PamelaSatterfield
- Math, feasible region
-
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