Question 1

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 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 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 4

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

Accepted Answer

A) True 
 B)False

Question 5

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 6

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 7

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 8

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. $$\begin{array} { c c c c } 
\text { Truck } & \text { Cost } & \begin{array} { c } 
\text { Capacity } \
( \text { Cu. Ft.) }
\end{array} & \begin{array} { c } 
\text { Drivers } \
\text { Needed }
\end{array} \
\hline \text { Small } & \$ 18,000 & 2,400 & 1 \
\text { Large } & \$ 45,000 & 6,000 & 3
\end{array}$$ 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 large
b

Question 9

Use this graph to answer the questions.   $$\begin{array} { l l } 
\operatorname { Max } \quad & 20 x + 10 y \
\text { s.t. } & 12 x + 15 y \leq 180 \
&15 x + 10 y \leq 150 \
&3 x - 8 y \leq 0 \
&x , y \geq 0
\end{array}$$ 
a.Which area (I, II, III, IV, or V) forms the feasible region?
b.Which point (A, B, C, D, or E) is optimal?
c.Which constraints are binding?
d.Which slack variables are zero?

Accepted Answer

a.Area III is the feasible reg

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

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 12

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Accepted Answer

A) proportionality 
B) additivity 
C) divisibility 
D) normality 
A) proportionality 
B) additivity 
C) divisibility 
D) normality

Question 13

Find the complete optimal solution to this linear programming problem.
 $$\begin{array} { l r } 
\text { Min } \quad & 5 x + 6 y \\
\
\text { s.t. } & 3 x + y \geq 15 \
& x + 2 y \geq 12 \
&3 x + 2 y \geq 24 \
& x , y \geq 0
\end{array}$$

Accepted Answer

@#IMG-DLM& The complete optima

Question 14

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 15

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 16

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1)or 125 wiffle balls (x2)can be produced per hour of labor,which of the following constraints reflects this situation?

Accepted Answer

A) 300x1 + 125x2 > 4,000 
B) 300x1 + 125x2 1 + x2) 1 + 125x2 = 4,000 
A) 300x1 + 125x2 > 4,000 
B) 300x1 + 125x2 1 + x2) 1 + 125x2 = 4,000

Question 17

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 18

Find the complete optimal solution to this linear programming problem.
 $$\begin{array} { l l } 
\text { Max } & 5 x + 3 y \
\
\text { s.t. } & 2 x + 3 y \leq 30 \
& 2 x + 5 y \leq 40 \
& 6 x - 5 y \leq 0 \
& x , y \geq 0
\end{array}$$

Accepted Answer

@#IMG-DLM& The complete optima

Question 19

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 20

For the following linear programming problem,determine the optimal solution by the graphical solution method.Are any of the constraints redundant? If yes,then identify the constraint that is redundant.
 $$\begin{array} { c c } 
\operatorname { Max } & x + 2 y \
\text { s.t. } & x + y \leq 3 \
& x - 2 y \geq 0 \
&y \leq 1 \
&x , y \geq 0
\end{array}$$

Accepted Answer

x = 2,and y = 1 Yes,

A constraint that does not affect the feasible region is a

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

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 unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

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

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

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

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

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Find the complete optimal solution to this linear programming problem. Min 5x+6y \ s.t. 3x+y\geq15 x+2y\geq12 3x+2y\geq24 x,y\geq0

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

Which of the following statements is not true?

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁)or 125 wiffle balls (x₂)can be produced per hour of labor,which of the following constraints reflects this situation?

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

Find the complete optimal solution to this linear programming problem. Max 5x+3y s.t. 2x+3y\leq30 2x+5y\leq40 6x-5y\leq0 x,y\geq0

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

For the following linear programming problem,determine the optimal solution by the graphical solution method.Are any of the constraints redundant? If yes,then identify the constraint that is redundant. Max x+2y s.t. x+y\leq3 x-2y\geq0 y\leq1 x,y\geq0

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

A constraint that does not affect the feasible region is a

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

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 unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

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

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

Use this graph to answer the questions. Max 20x+10y s.t. 12x+15y\leq180 15x+10y\leq150 3x-8y\leq0 x,y\geq0 a.Which area (I, II, III, IV, or V) forms the feasible region? b.Which point (A, B, C, D, or E) is optimal? c.Which constraints are binding? d.Which slack variables are zero?

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

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

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Find the complete optimal solution to this linear programming problem. Min 5x+6y \ s.t. 3x+y\geq15 x+2y\geq12 3x+2y\geq24 x,y\geq0

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

Which of the following statements is not true?

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1)or 125 wiffle balls (x2)can be produced per hour of labor,which of the following constraints reflects this situation?

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

Find the complete optimal solution to this linear programming problem. Max 5x+3y s.t. 2x+3y\leq30 2x+5y\leq40 6x-5y\leq0 x,y\geq0

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

For the following linear programming problem,determine the optimal solution by the graphical solution method.Are any of the constraints redundant? If yes,then identify the constraint that is redundant. Max x+2y s.t. x+y\leq3 x-2y\geq0 y\leq1 x,y\geq0

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

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁)or 125 wiffle balls (x₂)can be produced per hour of labor,which of the following constraints reflects this situation?