Finding Feasible Solutions To A Linear Programming Worksheet - Columbia University In The City Of New York Page 9
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14Standard Form
maximize
2x
3x
M a
M a
(29)
1
2
1
2
subject to
.5x
+ .25x
+ s
= 4
(30)
1
2
1
x
+
3x
e
+
a
= 20
(31)
1
2
1
1
x
+
x
+ a
= 10
(32)
1
2
2
x
, x
, s
, e
, a
, a
0 .
(33)
1
2
1
1
1
2
Now we convert it to standard form. Either a slack variable or an artificial
variable goes on the left hand side. We also will substitute for a
and a
in
1
2
the objective function. This yields:
z =
30M
+ (2M
2)x
+ (4M
3)x
M e
(34)
1
2
1
s
=
4
.5x
.25x
(35)
1
1
2
a
=
20
x
3x
+
e
(36)
1
1
2
1
a
=
10
x
x
(37)
2
1
2
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