Linear Programs
z
A
linear function
is a function of the form:
f(x
1
, x
2
, . . . , x
n
) = c
1
x
1
+ c
2
x
2
+ . . . + c
n
x
n
=
∑
i=1 to n
c
i
x
i
e.g.,
3x
1
+ 4x
2
 3x
4
.
z
A mathematical program is a
linear program (LP)
if the
objective is a linear function and the constraints are
linear equalities or inequalities.
e.g.,
3x
1
+
4x
2
 3x
4
≥
7
x
1

2x
5
= 7
z
Typically, an LP has nonnegativity constraints.
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