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+10X2

Subject to:

2X1<=10

2X1+4X2<=16

4X2<=8

X1=6

Formulation 2

Maximize X1+2X2

subject to:

X1<=1

2X2<=2

X1+2X2<=2

Formulation 3

Maximize 3X1+2X2

subject to:

X1+X2>=5

X1>=2

2X2>=8

Formulation 4

Maximize 3X1+3X2

subject to:

4X1+6X2<=48

4X1+2X2<=12

3X2>=3

2X1>=2

(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+10X2

Subject to:

2X1<=10

2X1+4X2<=16

4X2<=8

X1=6

Formulation 2

Maximize X1+2X2

subject to:

X1<=1

2X2<=2

X1+2X2<=2

Formulation 3

Maximize 3X1+2X2

subject to:

X1+X2>=5

X1>=2

2X2>=8

Formulation 4

Maximize 3X1+3X2

subject to:

4X1+6X2<=48

4X1+2X2<=12

3X2>=3

2X1>=2

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