Question 1

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

Accepted Answer

A)  optimal. 
B)  feasible. 
C)  infeasible. 
D)  semi-feasible. 
A)  optimal. 
B)  feasible. 
C)  infeasible. 
D)  semi-feasible.

Question 2

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

Accepted Answer

To put a linear program in standard form

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

​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 5

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

Accepted Answer

Infeasible or unbounded problems can be

Question 6

A linear programming problem can be both unbounded and infeasible.

Accepted Answer

A) True 
 B)False

Question 7

​Explain the concepts of proportionality, additivity, and divisibility.

Accepted Answer

Proportionality refers to the relationsh

Question 8

For the following linear programming problem, determine the optimal solution by the graphical solution method
Max
−X + 2Y
s.t.
6X − 2Y ≤ 3
−2X + 3Y ≤ 6
X + Y ≤ 3
X, Y ≥ 0

Accepted Answer

X = 0.6 an

Question 9

​Explain the difference between profit and contribution in an objective function. Why is it important for the decision
maker to know which of these the objective function coefficients represent?

Accepted Answer

Profit and contribution are two differen

Question 10

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 11

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 12

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

The standard form of a linear programming problem will have the same solution as the original problem.

Accepted Answer

A) True 
 B)False

Question 15

A redundant constraint is a binding constraint.

Accepted Answer

A) True 
 B)False

Question 16

Solve the following linear program by the graphical method.
Max
4X + 5Y
s.t.
X + 3Y ≤ 22
−X + Y ≤ 4
Y ≤ 6
2X − 5Y ≤ 0
X, Y ≥ 0

Accepted Answer

Two extreme points exist (Poin

Question 17

A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu. ft. Two types of trucks are appropriate for the specialized operation. Their characteristics and costs are summarized in the table below. Note that truck 2 requires 3 drivers for long haul trips. There are 41 potential drivers available and there are facilities for at most 40 trucks. The businessman's objective is to minimize the total cost outlay for trucks.   ​
Solve the problem graphically and note there are alternate optimal solutions. Which optimal solution: 
a.
uses only one type of truck?
b.
utilizes the minimum total number of trucks?
c.
uses the same number of small and large trucks?

Accepted Answer

​
a.35 small, 0 larg

Question 18

​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 19

​Create a linear programming problem with two decision variables and three constraints that will include both a slack
and a surplus variable in standard form. Write your problem in standard form.

Accepted Answer

The linear programming problem with two

Question 20

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.

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

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

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

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.

A linear programming problem can be both unbounded and infeasible.

Explain the concepts of proportionality, additivity, and divisibility.

For the following linear programming problem, determine the optimal solution by the graphical solution method Max −X + 2Y s.t. 6X − 2Y ≤ 3 −2X + 3Y ≤ 6 X + Y ≤ 3 X, Y ≥ 0

Explain the difference between profit and contribution in an objective function. Why is it important for the decision maker to know which of these the objective function coefficients represent?

Slack

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

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

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

The standard form of a linear programming problem will have the same solution as the original problem.

A redundant constraint is a binding constraint.

Solve the following linear program by the graphical method. Max 4X + 5Y s.t. X + 3Y ≤ 22 −X + Y ≤ 4 Y ≤ 6 2X − 5Y ≤ 0 X, Y ≥ 0

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

Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form. Write your problem in standard form.

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

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

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

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

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

​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.

A linear programming problem can be both unbounded and infeasible.

​Explain the concepts of proportionality, additivity, and divisibility.

For the following linear programming problem, determine the optimal solution by the graphical solution method Max −X + 2Y s.t. 6X − 2Y ≤ 3 −2X + 3Y ≤ 6 X + Y ≤ 3 X, Y ≥ 0

​Explain the difference between profit and contribution in an objective function. Why is it important for the decision maker to know which of these the objective function coefficients represent?

Slack

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

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

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

The standard form of a linear programming problem will have the same solution as the original problem.

A redundant constraint is a binding constraint.

Solve the following linear program by the graphical method. Max 4X + 5Y s.t. X + 3Y ≤ 22 −X + Y ≤ 4 Y ≤ 6 2X − 5Y ≤ 0 X, Y ≥ 0

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

​Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form. Write your problem in standard form.

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

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

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

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

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.

Explain the concepts of proportionality, additivity, and divisibility.

Explain the difference between profit and contribution in an objective function. Why is it important for the decision maker to know which of these the objective function coefficients represent?

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

Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form. Write your problem in standard form.