1. Consider the following linear programming model (different objective function from question #15)

Minimize: Z = 3X1 + 2 X2

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

2. Consider the following linear programming model (one different constraint from problem #17):

Minimize: Z = 3X1 + 2X2

Constraints:

X1 + X2 4

X2 3

X1 3

X1, X2 0

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

a. (4,0)

b. (3,0)

c. (3,1)

d. (3,4)

e. no optimal solution

f. multiple optimal solutions

3. Problems #1 and #2 are the same linear programming model except for one constraint. In Problem #1 the third constraint is X₁ >= 2 and in Problem #2 the third constraint is X₁ >= 3, which is an increase of one unit. Note the change in the objective function value from problem #1 to problem #2. What is the shadow price?
   4. -1
   5. 0
   6. 1
   7. 3
   8. None of the above 4.Consider the following linear programming model

Maximize: Z = X1 + X2

Constraints:

X1 + X2 2

X1 1

X2 3

X1, X2 0

This linear programming model has:

a. one unique optimal solution

b. no feasible solutions

c. four binding constraints

d. two unique solutions

e. an unbounded feasible region