AMS 540 / MBA 540 (Fall, 2010)
Estie Arkin
Homework Set # 3: Solution notes
1).
(a). State a non degenerate BFS for the following LP: (make sure to say which variables are
basic, which are non basic and what is variable is equal to.)
max
z
= 6
x
1
+ 4
x
2
+
x
3
s
.
t
.
x
1
+
x
2
+
x
3
≤
1
x
1
≤
1
x
1
, x
2
, x
3
≥
0
Introduce slack variables
s
1
,s
2
in the first and second constraints to get standard form (remem
ber that Basic Solutions are defined only for standard form).
max
z
= 6
x
1
+ 4
x
2
+
x
3
s
.
t
.
x
1
+
x
2
+
x
3
+
s
1
= 1
x
1
+
s
2
= 1
x
1
, x
2
, x
3
, s
1
, s
2
≥
0
Let a BFS be
s
1
=
s
2
= 1 basic variables (non degenerate) and
x
1
=
x
2
=
x
3
= 0 non basic.
(Recall, the number of basic variables must be
m
, the number of constraints, which is 2 in our
case.)
(b). State a degenerate BFS for the LP in part (a). Basic variables
x
1
= 1 and
x
2
= 0 (degenerate),
x
3
=
s
1
=
s
2
= 0 non basic.
2).
(a). The current BFS is optimal.
c
1
≤
0,
c
2
≤
0, (optimality)
b
≥
0 (feasible).
(b). The current basic solution is not feasible.
b <
0.
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 Fall '08
 Arkin,E
 Operations Research, Want, BMW Sports Activity Series, LP, Mathematics in medieval Islam

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