Question 1

​In what part(s)of a linear programming formulation would the decision variables be stated?

Accepted Answer

A) ​objective function and the left-hand side of each constraint 
B) ​objective function and the right-hand side of each constraint 
C) ​the left-hand side of each constraint only 
D) ​the objective function only 
A) ​objective function and the left-hand side of each constraint 
B) ​objective function and the right-hand side of each constraint 
C) ​the left-hand side of each constraint only 
D) ​the objective function only

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

A linear programming problem can be both unbounded and infeasible.

Accepted Answer

A) True 
 B)False

Question 4

​A redundant constraint results in

Accepted Answer

A) ​no change in the optimal solution(s) 
B) ​an unbounded solution 
C) ​no feasible solution 
D) ​alternative optimal solutions 
A) ​no change in the optimal solution(s) 
B) ​an unbounded solution 
C) ​no feasible solution 
D) ​alternative optimal solutions

Question 5

Because surplus variables represent the amount by which the solution exceeds a minimum target,they are given positive coefficients in the objective function.

Accepted Answer

A) True 
 B)False

Question 6

The constraint 5x1 − 2x2 ≤ 0 passes through the point (20,50).

Accepted Answer

A) True 
 B)False

Question 7

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 8

An infeasible problem is one in which the objective function can be increased to infinity.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

​Explain the steps necessary to put a linear program in standard form.

Accepted Answer

To put a linear program in standard form

Question 11

​A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is

Accepted Answer

A) ​a standard variable 
B) ​a slack variable 
C) ​a surplus variable 
D) ​a non-negative variable 
A) ​a standard variable 
B) ​a slack variable 
C) ​a surplus variable 
D) ​a non-negative variable

Question 12

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 13

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

Accepted Answer

A) standard form. 
B) bounded form. 
C) feasible form. 
D) alternative form. 
A) standard form. 
B) bounded form. 
C) feasible form. 
D) alternative form.

Question 14

Alternative optimal solutions occur when there is no feasible solution to the problem.

Accepted Answer

A) True 
 B)False

Question 15

​Explain what to look for in problems that are infeasible or unbounded.

Accepted Answer

Infeasible or unbounded problems can be

Question 16

Only binding constraints form the shape (boundaries)of the feasible region.

Accepted Answer

A) True 
 B)False

Question 17

The constraint 2x1 − x2 = 0 passes through the point (200,100).

Accepted Answer

A) True 
 B)False

Question 18

Slack

Accepted Answer

A) is the difference between the left and right sides of a constraint. 
B) is the amount by which the left side of a ≤ constraint is smaller than the right side. 
C) is the amount by which the left side of a ≥ constraint is larger than the right side. 
D) exists for each variable in a linear programming problem. 
A) is the difference between the left and right sides of a constraint. 
B) is the amount by which the left side of a ≤ constraint is smaller than the right side. 
C) is the amount by which the left side of a ≥ constraint is larger than the right side. 
D) exists for each variable in a linear programming problem.

Question 19

A constraint that does not affect the feasible region is a

Accepted Answer

A) non-negativity constraint. 
B) redundant constraint. 
C) standard constraint. 
D) slack constraint. 
A) non-negativity constraint. 
B) redundant constraint. 
C) standard constraint. 
D) slack constraint.

Question 20

When you encounter infeasibility,making changes in the coefficients of the objective function will not help.

Accepted Answer

A) True 
 B)False

In what part(s)of a linear programming formulation would the decision variables be stated?

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

A linear programming problem can be both unbounded and infeasible.

A redundant constraint results in

Because surplus variables represent the amount by which the solution exceeds a minimum target,they are given positive coefficients in the objective function.

The constraint 5x₁ − 2x₂ ≤ 0 passes through the point (20,50).

Decision variables

An infeasible problem is one in which the objective function can be increased to infinity.

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

Explain the steps necessary to put a linear program in standard form.

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is

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

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

Alternative optimal solutions occur when there is no feasible solution to the problem.

Explain what to look for in problems that are infeasible or unbounded.

Only binding constraints form the shape (boundaries)of the feasible region.

The constraint 2x₁ − x₂ = 0 passes through the point (200,100).

Slack

A constraint that does not affect the feasible region is a

When you encounter infeasibility,making changes in the coefficients of the objective function will not help.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 7: Intro to Linear Programming

​In what part(s)of a linear programming formulation would the decision variables be stated?

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

A linear programming problem can be both unbounded and infeasible.

​A redundant constraint results in

Because surplus variables represent the amount by which the solution exceeds a minimum target,they are given positive coefficients in the objective function.

The constraint 5x1 − 2x2 ≤ 0 passes through the point (20,50).

Decision variables

An infeasible problem is one in which the objective function can be increased to infinity.

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

​Explain the steps necessary to put a linear program in standard form.

​A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is

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

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

Alternative optimal solutions occur when there is no feasible solution to the problem.

​Explain what to look for in problems that are infeasible or unbounded.

Only binding constraints form the shape (boundaries)of the feasible region.

The constraint 2x1 − x2 = 0 passes through the point (200,100).

Slack

A constraint that does not affect the feasible region is a

When you encounter infeasibility,making changes in the coefficients of the objective function will not help.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

In what part(s)of a linear programming formulation would the decision variables be stated?

A redundant constraint results in

The constraint 5x₁ − 2x₂ ≤ 0 passes through the point (20,50).

Explain the steps necessary to put a linear program in standard form.

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is

Explain what to look for in problems that are infeasible or unbounded.

The constraint 2x₁ − x₂ = 0 passes through the point (200,100).