=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 Formulation 3 Maximize subject to 10 10 2 10 2 4 16 4 8 6

1 2 1

1 2 2

1 X X X

X X X

X

+

≤

+ ≤

≤

=

Maximize subject to 3 2 5

2 2 8 1 2 1 2 1

2 X X X X X

X

+

+ ≥

≥

≥

Formulation 2 Formulation 4 Maximize subject to X X X

X X X 1 2 1

2 1 2 2

1 2 2 2 2

+

≤

≤

+ ≤

Maximize subject to 3 3 4 6 48 4 2 12 3 3 2 2 1 2 1 2 1 2 2

1 X X X X X X X

X

+

+ ≤

+ ≤

≥

≥