Question 1

Find the complete optimal solution to this linear programming problem.
Min
3X + 3Y
s.t.
12X + 4Y ≥ 48
10X + 5Y ≥ 50
4X + 8Y ≥ 32
X , Y ≥ 0

Accepted Answer

The complete optimal solution is X = 4, Y = 2, Z = 18, S₁ = 8, S₂ = 0, S₃ = 0

Question 2

Consider the following linear program:
Max
60X + 43Y
s.t.
X + 3Y ≥ 9
6X − 2Y = 12
X + 2Y ≤ 10
X, Y ≥ 0
​
a.
Write the problem in standard form.
b.
What is the feasible region for the problem?
c.
Show that regardless of the values of the actual objective function coefficients, the optimal solution will occur at one of two points. Solve for these points and then determine which one maximizes the current objective function.

Accepted Answer

a.Max
60X + 43Y
s.t.
X + 3Y − S₁ = 9
6X − 2Y = 12
X + 2Y + S₃ = 10
X, Y, S₁, S₃ ≥ 0
B.Line segment of 6X − 2Y = 12 between (22/7,24/7) and (27/10,21/10).
C.Extreme points: (22/7,24/7) and (27/10,21/10). First one is optimal, giving Z = 336.

Question 3

As long as the slope of the objective function stays between the slopes of the binding constraints

Accepted Answer

A)  the value of the objective function won't change. 
B)  there will be alternative optimal solutions. 
C)  the values of the dual variables won't change. 
D)  there will be no slack in the solution. 
A)  the value of the objective function won't change. 
B)  there will be alternative optimal solutions. 
C)  the values of the dual variables won't change. 
D)  there will be no slack in the solution. C

Question 4

All linear programming problems have all of the following properties EXCEPT

Accepted Answer

A)  a linear objective function that is to be maximized or minimized. 
B)  a set of linear constraints. 
C)  alternative optimal solutions. 
D)  variables that are all restricted to nonnegative values. 
A)  a linear objective function that is to be maximized or minimized. 
B)  a set of linear constraints. 
C)  alternative optimal solutions. 
D)  variables that are all restricted to nonnegative values.

Question 5

Consider the following linear programming problem
Max
8X + 7Y
s.t.
15X + 5Y ≤ 75
10X + 6Y ≤ 60
X + Y ≤ 8
X, Y ≥ 0
​
a.Use a graph to show each constraint and the feasible region.
b.Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?
c.What is the optimal value of the objective function?

Accepted Answer

a. @#IMG-DLM& B.The optimal solution occ

Question 6

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Accepted Answer

A)  alternate optimality 
B)  infeasibility 
C)  unboundedness 
D)  each case requires a reformulation. 
A)  alternate optimality 
B)  infeasibility 
C)  unboundedness 
D)  each case requires a reformulation.

Question 7

To find the optimal solution to a linear programming problem using the graphical method

Accepted Answer

A)  find the feasible point that is the farthest away from the origin. 
B)  find the feasible point that is at the highest location. 
C)  find the feasible point that is closest to the origin. 
D)  None of the alternatives is correct. 
A)  find the feasible point that is the farthest away from the origin. 
B)  find the feasible point that is at the highest location. 
C)  find the feasible point that is closest to the origin. 
D)  None of the alternatives is correct.

Question 8

The improvement in the value of the objective function per unit increase in a right-hand side is the

Accepted Answer

A)  sensitivity value. 
B)  dual price. 
C)  constraint coefficient. 
D)  slack value. 
A)  sensitivity value. 
B)  dual price. 
C)  constraint coefficient. 
D)  slack value.

Question 9

A range of optimality is applicable only if the other coefficient remains at its original value.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following is a valid objective function for a linear programming problem?

Accepted Answer

A)  Max 5xy 
B)  Min 4x + 3y + (2/3)z 
C)  Max 5x2 + 6y2 
D)  Min (x1 + x2)/x3 
A)  Max 5xy 
B)  Min 4x + 3y + (2/3)z 
C)  Max 5x2 + 6y2 
D)  Min (x1 + x2)/x3

Question 11

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Accepted Answer

A) True 
 B)False

Question 12

Which of the following statements is NOT true?

Accepted Answer

A)  A feasible solution satisfies all constraints. 
B)  An optimal solution satisfies all constraints. 
C)  An infeasible solution violates all constraints. 
D)  A feasible solution point does not have to lie on the boundary of the feasible region. 
A)  A feasible solution satisfies all constraints. 
B)  An optimal solution satisfies all constraints. 
C)  An infeasible solution violates all constraints. 
D)  A feasible solution point does not have to lie on the boundary of the feasible region.

Question 13

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain.
Min
3X + 3Y
s.t.
1X + 2Y ≤ 16
1X + 1Y ≤ 10
5X + 3Y ≤ 45
X , Y ≥ 0

Accepted Answer

The proble

Question 14

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Accepted Answer

A) True 
 B)False

Question 15

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.

Accepted Answer

A) True 
 B)False

Question 16

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Accepted Answer

A) True 
 B)False

Question 17

Decision variables

Accepted Answer

A)  tell how much or how many of something to produce, invest, purchase, hire, etc. 
B)  represent the values of the constraints. 
C)  measure the objective function. 
D)  must exist for each constraint. 
A)  tell how much or how many of something to produce, invest, purchase, hire, etc. 
B)  represent the values of the constraints. 
C)  measure the objective function. 
D)  must exist for each constraint.

Question 18

All of the following statements about a redundant constraint are correct EXCEPT

Accepted Answer

A)  A redundant constraint does not affect the optimal solution. 
B)  A redundant constraint does not affect the feasible region. 
C)  Recognizing a redundant constraint is easy with the graphical solution method. 
D)  At the optimal solution, a redundant constraint will have zero slack. 
A)  A redundant constraint does not affect the optimal solution. 
B)  A redundant constraint does not affect the feasible region. 
C)  Recognizing a redundant constraint is easy with the graphical solution method. 
D)  At the optimal solution, a redundant constraint will have zero slack.

Question 19

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Accepted Answer

A) True 
 B)False

Question 20

The maximization or minimization of a quantity is the

Accepted Answer

A)  goal of management science. 
B)  decision for decision analysis. 
C)  constraint of operations research. 
D)  objective of linear programming. 
A)  goal of management science. 
B)  decision for decision analysis. 
C)  constraint of operations research. 
D)  objective of linear programming.

Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y ≥ 48 10X + 5Y ≥ 50 4X + 8Y ≥ 32 X , Y ≥ 0

As long as the slope of the objective function stays between the slopes of the binding constraints

All linear programming problems have all of the following properties EXCEPT

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

To find the optimal solution to a linear programming problem using the graphical method

The improvement in the value of the objective function per unit increase in a right-hand side is the

A range of optimality is applicable only if the other coefficient remains at its original value.

Which of the following is a valid objective function for a linear programming problem?

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Which of the following statements is NOT true?

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 3X + 3Y s.t. 1X + 2Y ≤ 16 1X + 1Y ≤ 10 5X + 3Y ≤ 45 X , Y ≥ 0

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

The point (3, 2) is feasible for the constraint 2x₁ + 6x₂ ≤ 30.

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Decision variables

All of the following statements about a redundant constraint are correct EXCEPT

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

The maximization or minimization of a quantity is the

Introduction

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 2: An Introduction to Linear Programming

Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y ≥ 48 10X + 5Y ≥ 50 4X + 8Y ≥ 32 X , Y ≥ 0

As long as the slope of the objective function stays between the slopes of the binding constraints

All linear programming problems have all of the following properties EXCEPT

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

To find the optimal solution to a linear programming problem using the graphical method

The improvement in the value of the objective function per unit increase in a right-hand side is the

A range of optimality is applicable only if the other coefficient remains at its original value.

Which of the following is a valid objective function for a linear programming problem?

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Which of the following statements is NOT true?

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 3X + 3Y s.t. 1X + 2Y ≤ 16 1X + 1Y ≤ 10 5X + 3Y ≤ 45 X , Y ≥ 0

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Decision variables

All of the following statements about a redundant constraint are correct EXCEPT

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

The maximization or minimization of a quantity is the

Introduction

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

The point (3, 2) is feasible for the constraint 2x₁ + 6x₂ ≤ 30.