7-27
Consider the following four LP formulations. Using a graphical approach,
determine
(a)
which formulation has more than one optimal solution.
(b)
which formulation is unbounded.
(c)
which formulation has no feasible solution.
(d)
which formulation is correct as is.
Formulation
1
Maximize
10X1 + 10
X2
subject
to 2 X1 ≤10
2
X1 + 4 X2 ≤16
4 X2 ≤ 8
X1
= 6
Formulation
2
Maximize
X1 + 2 X2
subject
to X1 ≤ 1
2 X2 ≤
2
X1
+ 2 X2 ≤ 2
Formulation
3
Maximize
10 X1 + 10 X2
subject
to X1 + X2 ≥ 5
X1 ≥ 2
2
X2 ≥ 8
Formulation 4
Maximize
3 X1 + 3 X2
subject
to 4 X1 + 6 X2 ≤ 48
4 X1 + 2 X2 ≤
12
3 X2 ≥ 3
2
X1 ≥
2
Solution
(a)
which formulation has more than one optimal solution.
Formulation 2
(b)
which formulation is unbounded.
Formulation 3
(c)
which formulation has no feasible solution.
Formulation
1
(d)
which formulation is correct as is.
Formulation
4
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