1.Consider the following optimization model:

Maximize: Z = X₁ - X₂+ 3X₃

Constraints:

X³₁ + X₂ - X₃ 357

3X₁ - 6X₂ - 8X₃ 125

-5X₁ - 2X₂ - 7X₃ -1033

X₁, X₂, X₃ 0

This optimization model fails to be a linear programming model because it violates which of the following assumptions?

a. non-negativity

b. linearity

c. divisibility

d. certainty

e. non-negativity and linearity

2. Consider the following linear programming model:

Maximize: Z = 2X1 + 3X2

Constraints:

X1 2

X2 3

X1 1

X1, X2 0

The solution to this linear programming model in the format (X₁, X₂) is:

a. (0,0)

b. (0,3)

c. (1,3)

d. (2,3)

e. (2,0)

f. (1,0)

g. b & e

h. c & d

3. Consider the following linear programming model:

Minimize: Z = 2X1 + 3X2

Constraints:

X1 2

X2 3

X1 1

X1, X2 0

The solution to this linear programming model in the format (X₁, X₂) is:

a. (0,0)

b. (0,3)

c. (1,3)

d. (2,3)

e. (2,0)

f. (1,0)

g. no optimal solution

4. Consider the following linear programming model

Maximize: Z = 2X1 + 3X2

Constraints:

X1 + X2 4

X2 3

X1 2

X1, X2 0

This linear programming model has:

a. no feasible solutions

b. an infinite number of feasible solutions

c. an unbounded feasible region

d. one unique optimal solution

e. a & c

f. b & c

g. none of the above

5. Consider the following linear programming model.

Minimize: Z = 2X1 + 3X2

Constraints:

X1 + X2 4

X2 3

X1 2

X1, X2 0

The optimal solution to this linear programming model in the format (X₁, X₂) is:

a. (4,0)

b. (2,2)

c. (2,3)

d. (0,0)

e. no optimal solution

f. multiple optimal solutions

6. Consider the following linear programming model (same model as question #15)

Minimize: Z = 2X1 + 3X2

Constraints:

X1 + X2 4

X2 3

X1 2

X1, X2 0

A feasible solution to this linear programming model in the format (X₁, X₂) is:

a. (4,2)

b. (3,4)

c. (0,2)

d. (3,0)

e. no feasible solution