# Quiz on Linear Programming Models: Graphical and Computer Methods

**Pages:**17 (2781 words)

**Published:**January 11, 2015

Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 2 Linear Programming Models: Graphical and Computer Methods

2.1 Chapter Questions

1) Consider the following linear programming model:

MaxX12 + X2 + 3X3

Subject to:

X1 + X2 ≤ 3

X1 + X2 ≤ 1

X1, X2 ≥ 0

This problem violates which of the following assumptions?

A) certainty

B) proportionality

C) divisibility

D) linearity

E) integrality

Answer: D

Page Ref: 22

Topic: Developing a Linear Programming Model

Difficulty: Easy

2) Consider the following linear programming model:

Min2X1 + 3X2

Subject to:

X1 + 2X2 ≤ 1

X2 ≤ 1

X1 ≥ 0, X2 ≤ 0

This problem violates which of the following assumptions?

A) additivity

B) divisibility

C) non-negativity

D) proportionality

E) linearity

Answer: C

Page Ref: 21

Topic: Developing a Linear Programming Model

Difficulty: Easy

3) A redundant constraint is eliminated from a linear programming model. What effect will this have on the optimal solution? A) feasible region will decrease in size

B) feasible region will increase in size

C) a decrease in objective function value

D) an increase in objective function value

E) no change

Answer: E

Page Ref: 36

Topic: Special Situations in Solving Linear Programming Problems Difficulty: Moderate

4) Consider the following linear programming model:

Max2X1 + 3X2

Subject to:

X1 ≤ 2

X2 ≤ 3

X1 ≤ 1

X1, X2 ≥ 0

This linear programming model has:

A) alternate optimal solutions

B) unbounded solution

C) redundant constraint

D) infeasible solution

E) non-negative solution

Answer: C

Page Ref: 36

Topic: Special Situations in Solving Linear Programming Problems Difficulty: Moderate

5) A linear programming model generates an optimal solution with fractional values. This solution satisfies which basic linear programming assumption? A) certainty

B) divisibility

C) proportionality

D) linearity

E) non-negativity

Answer: B

Page Ref: 22

Topic: Developing a Linear Programming Model

Difficulty: Moderate

6) Consider the following linear programming model:

MaxX1 + X2

Subject to:

X1 + X2 ≤ 2

X1 ≥ 1

X2 ≥ 3

X1, X2 ≥ 0

This linear programming model has:

A) alternate optimal solution

B) unbounded solution

C) redundant constraint

D) infeasible solution

E) unique solution

Answer: D

Page Ref: 37

Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy

7) Consider the following linear programming model

Max 2X1 + 3X2

Subject to:

X1 + X2

X1 ≥ 2

X1, X2 0

This linear programming model has:

A) redundant constraints

B) infeasible solution

C) alternate optimal solution

D) unique solution

E) unbounded solution

Answer: E

Page Ref: 39

Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy

8) Consider the following linear programming model

Min2X1 + 3X2

Subject to:

X1 + X2 ≥ 4

X1 ≥ 2

X1, X2 0

This linear programming model has:

A) unique optimal solution

B) unbounded solution

C) infeasible solution

D) alternate optimal solution

E) redundant constraints

Answer: A

Page Ref: 38

Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy

Figure 1:

Figure 1 demonstrates an Excel spreadsheet that is used to model the following linear programming problem:

Max:4 X1 + 3 X2

Subject to:

3 X1 +5 X2 ≤ 40

12 X1 + 10 X2 ≤ 120

X1 ≥ 15

X1, X2 ≥ 0

Note: Cells B3 and C3 are the designated cells for the optimal values of X1 and X2, respectively, while cell E4 is the designated cell for the objective function value. Cells D8:D10 designate the left-hand side of the constraints.

9) Refer to Figure 1. What formula should be entered in cell E4 to compute total profitability? A) =SUMPRODUCT(B5:C5,B2:C2)

B) =SUM(B3:C3)

C) =B2*B5 + C2*C5

D) =SUMPRODUCT(B5:C5,E8:E10)

E) =B3*B5 + C3*C5

Answer: E

Page Ref: 42

Topic: Setting Up and Solving Linear Programming Problems...

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