Question 1

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

Question 2

Maxwell Manufacturing makes two models of felt tip marking pens.Requirements for each lot of pens are given below. $$\begin{array} { l | c c | c } 
& \text { Fliptop Model } & \text { Tiptop Model } & \text { Available } \
\hline \text { Plastic } & 3 & 4 & 36 \
\text { Ink Assembly } & 5 & 4 & 40 \
\text { Molding Time } & 5 & 2 & 30
\end{array}$$ The profit for either model is $1000 per lot. 
a.What is the linear programming model for this problem?
b.Find the optimal solution.
c.Will there be excess capacity in any resource?

Accepted Answer

a.Let F = the number of lots of Fliptop pens to produce Let T = the number of lots of Tiptop pens to produce $$\begin{array} { c r } \text { Max } & 1000 F + 1000 T \ \text { s.t. } & 3 F + 4 T \leq 36 \ & 5 F + 4 T \leq 40 \ & 5 F + 2 T \leq 30 \ &\mathrm {~F} , T \geq 0 \end{array}$$ b. The complete optimal solution is F = 2,T = 7.5,s₁ = 0,s₂ = 0,s₃ = 5,obj.func.= 9500 c.There is an excess of 5 units of molding time available.

Question 3

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. B

Question 4

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

Accepted Answer

A) True 
 B)False

Question 5

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.

Question 6

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 7

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 F1F1F1S1F1F1F10 constraint is smaller than the right side. 
C) is the amount by which the left side of a F1F1F1S1F1F1F10 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 F1F1F1S1F1F1F10 constraint is smaller than the right side. 
C) is the amount by which the left side of a F1F1F1S1F1F1F10 constraint is larger than the right side. 
D) exists for each variable in a linear programming problem.

Question 8

In a feasible problem,an equal-to constraint cannot be nonbinding.

Accepted Answer

A) True 
 B)False

Question 9

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain.
 $$\begin{array} { l l } 
\text { Min } & 3 x + 3 y \
\text { s.t. } & 1 x + 2 y \leq 16 \
& 1 x + 1 y \leq 10 \
& 5 x + 3 y \leq 45 \
& x , y \geq 0
\end{array}$$

Accepted Answer

The proble

Question 10

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 11

Find the complete optimal solution to this linear programming problem.
 $$\begin{array} { ll } 
\operatorname { Max }& 2 x + 3 y \
\
\text { s.t. } & 4 x + 9 y \leq 72 \
&10 x + 11 y \leq 110 \
&17 x + 9 y \leq 153 \
&x , y \geq 0 \
\end{array}$$

Accepted Answer

@#IMG-DLM& The complete optima

Question 12

Solve the following system of simultaneous equations.
6x + 2y = 50
2x + 4y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.
6x...

Question 13

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 14

Explain how to graph the line x1 F1F1F1S1F1F1F10 2x2 F1F1F1S1F1F1F10 0.

Accepted Answer

To graph the line 2x + 1 = 0, we can sta

Question 15

Solve the following system of simultaneous equations.
6x + 4y = 40
2x + 3y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.
6x...

Question 16

A linear programming problem can be both unbounded and infeasible.

Accepted Answer

A) True 
 B)False

Question 17

A redundant constraint is a binding constraint.

Accepted Answer

A) True 
 B)False

Question 18

The constraint 5x1 F1F1F1S1F1F1F10 2x2 F1F1F1S1F1F1F10 0 passes through the point (20,50).

Accepted Answer

A) True 
 B)False

Question 19

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.

Question 20

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

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

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

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

The maximization or minimization of a quantity is the

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.

Slack

In a feasible problem,an equal-to constraint cannot be nonbinding.

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain. Min 3x+3y s.t. 1x+2y\leq16 1x+1y\leq10 5x+3y\leq45 x,y\geq0

A redundant constraint results in

Find the complete optimal solution to this linear programming problem. Max 2x+3y s.t. 4x+9y\leq72 10x+11y\leq110 17x+9y\leq153 x,y\geq0

Solve the following system of simultaneous equations. 6x + 2y = 50 2x + 4y = 20

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

Explain how to graph the line x₁  2x₂  0.

Solve the following system of simultaneous equations. 6x + 4y = 40 2x + 3y = 20

A linear programming problem can be both unbounded and infeasible.

A redundant constraint is a binding constraint.

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

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

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

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 7: Introduction to Linear Programming

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

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

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

The maximization or minimization of a quantity is the

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.

Slack

In a feasible problem,an equal-to constraint cannot be nonbinding.

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain. Min 3x+3y s.t. 1x+2y\leq16 1x+1y\leq10 5x+3y\leq45 x,y\geq0

A redundant constraint results in

Find the complete optimal solution to this linear programming problem. Max 2x+3y s.t. 4x+9y\leq72 10x+11y\leq110 17x+9y\leq153 x,y\geq0

Solve the following system of simultaneous equations. 6x + 2y = 50 2x + 4y = 20

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

Explain how to graph the line x1  2x2  0.

Solve the following system of simultaneous equations. 6x + 4y = 40 2x + 3y = 20

A linear programming problem can be both unbounded and infeasible.

A redundant constraint is a binding constraint.

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

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

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

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Explain how to graph the line x₁  2x₂  0.

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