Question 1

The simplex method is a general mathematical solution technique for solving linear programming problems.

Accepted Answer

A) True 
 B)False  True

Question 2

The simplex method is a general mathematical solution technique for solving ________ programming problems.

Accepted Answer

A)  integer 
B)  non-linear 
C)  linear 
D)  A, B, and C 
A)  integer 
B)  non-linear 
C)  linear 
D)  A, B, and C C

Question 3

Consider the following linear programming problem and the corresponding final tableau.
$\begin{array} { l l } 
\text { MAX } & Z = 3 x _ { 1 } + 5 x _ { 2 } \
\text { s.t. } & x _ { 1 } \leq 4 \
& 2 x _ { 2 } \leq 12 \
& 3 x _ { 1 } + 2 x _ { 2 } \geq 18
\end{array}$

What is the shadow price for each constraint?

Accepted Answer

constraint 1, 3; constraint 2, 2.5; constraint 3, 0

Question 4

If the primal problem has three constraints, then the corresponding dual problem will have three ________.

Accepted Answer

The answer of If the primal problem has three constraints,...

Question 5

Consider the following linear programming problem:
$\begin{array} { l l } 
\text { MAX } & \mathrm { Z } = 10 x _ { 1 } + 30 x _ { 2 } \
\text { s.t. } & 4 x _ { 1 } + 6 x _ { 2 } \leq 12 \
& 8 x _ { 1 } + 4 x _ { 2 } \leq 16
\end{array}$

Use the two tables below to create the initial tableau and perform 1 pivot.

Accepted Answer

The answer of Consider the following linear programming problem:
\(\begin{array} {...

Question 6

Slack variables are added to constraints and represent unused resources.

Accepted Answer

A) True 
 B)False

Question 7

Write the dual form of the following linear program.

$\begin{array} { l l } 
\text { MAX } & \mathrm { Z } = 3 x _ { 1 } + 5 x _ { 2 } \
\text { s.t. } & x _ { 1 } \leq 4 \
& 2 x _ { 2 } \leq 12 \
& 3 x _ { 1 } + 2 x _ { 2 } \geq 18
\end{array}$

Accepted Answer

MIN Zd = 4y1 + 12y2

Question 8

Artificial variables are added to constraints and represent unused resources.

Accepted Answer

A) True 
 B)False

Question 9

In solving a linear programming problem with simplex method, the number of basic variables is the same as the number of constraints in the original problem

Accepted Answer

A) True 
 B)False

Question 10

The ________ step in solving a linear programming model manually with the simplex method is to convert the model into standard form.

Accepted Answer

A)  first 
B)  second 
C)  last 
D)  only 
A)  first 
B)  second 
C)  last 
D)  only

Question 11

Given the following linear programming problem:
$\begin{array} { l l } 
\operatorname { maximize } & \mathrm { Z } = \$ 100 x _ { 1 } + 80 x _ { 2 } \
\text { subject to } & x _ { 1 } + 2 x _ { 2 } \leq 40 \
& 3 x _ { 1 } + x _ { 2 } \leq 60 \
& x _ { 1 } , x _ { 2 } \geq 0
\end{array}$
Using the simplex method, what is the optimal value for the objective function?

Accepted Answer

The answer of Given the following linear programming problem:
\(\begin{array} {...

Question 12

The leaving variable is determined by dividing the quantity values by the pivot column values and selecting the

Accepted Answer

A)  maximum positive value. 
B)  minimum negative value. 
C)  minimum positive value. 
D)  maximum negative value. 
A)  maximum positive value. 
B)  minimum negative value. 
C)  minimum positive value. 
D)  maximum negative value.

Question 13

The simplex method cannot be used to solve quadratic programming problems.

Accepted Answer

A) True 
 B)False

Question 14

Given the following linear programming problem:
$\begin{array} { l l } 
\operatorname { maximize } & 4 x _ { 1 } + 3 x _ { 2 } \
\text { subject to } & 4 x _ { 1 } + 3 x _ { 2 } \leq 23 \
& 5 x _ { 1 } - x _ { 2 } \leq 5 \
& x _ { 1 } , x _ { 2 } \geq 0
\end{array}$
What is the (Ci- Zi) value for S2 at the initial solution?

Accepted Answer

The answer of Given the following linear programming problem:
\(\begin{array} {...

Question 15

________ in linear programming is when a basic variable takes on a value of zero (i.e., a zero in the right-hand side of the constraints of the tableau).

Accepted Answer

The answer of ________ in linear programming is when a...

Question 16

When solving a linear programming problem, a decision variable that leaves the basis in one iteration of the simplex method can return to the basis on a later iteration.

Accepted Answer

A) True 
 B)False

Question 17

The simplex method does not guarantee an integer solution.

Accepted Answer

A) True 
 B)False

Question 18

Row operations are used to solve simultaneous equations where equations are multiplied by constants and added or subtracted from each other.

Accepted Answer

A) True 
 B)False

Question 19

Solve the following problem using the simplex method.
$\begin{array} { l } 
\text { Minimize } \mathrm { Z } = 2 x _ { 1 } + 6 x _ { 2 } \
\text { Subject to: } \quad 2 x _ { 1 } + 4 x _ { 2 } \leq 12 \
\qquad 3 x _ { 1 } + 2 x _ { 2 } \geq 9 \
x _ { 1 } , x _ { 2 } \geq 0
\end{array}$

Accepted Answer

x₁ = 1.5,

Question 20

Given the following linear programming problem:
$\begin{array} { l l } 
\operatorname { maximize } & 4 x _ { 1 } + 3 x _ { 2 } \
\text { subject to } & 4 x _ { 1 } + 3 x _ { 2 } \leq 23 \
& 5 x _ { 1 } - x _ { 2 } \leq 5 \
& x _ { 1 } , x _ { 2 } \geq 0
\end{array}$
What is the value of x2 in the final tableau?

Accepted Answer

The answer of Given the following linear programming problem:
\(\begin{array} {...

The simplex method is a general mathematical solution technique for solving linear programming problems.

The simplex method is a general mathematical solution technique for solving ________ programming problems.

If the primal problem has three constraints, then the corresponding dual problem will have three ________.

Slack variables are added to constraints and represent unused resources.

Write the dual form of the following linear program. MAX =3+5 s.t. \leq4 2\leq12 3+2\geq18

Artificial variables are added to constraints and represent unused resources.

In solving a linear programming problem with simplex method, the number of basic variables is the same as the number of constraints in the original problem

The ________ step in solving a linear programming model manually with the simplex method is to convert the model into standard form.

Given the following linear programming problem: maximize =\ 100+80 subject to +2\leq40 3+\leq60 ,\geq0 Using the simplex method, what is the optimal value for the objective function?

The leaving variable is determined by dividing the quantity values by the pivot column values and selecting the

The simplex method cannot be used to solve quadratic programming problems.

Given the following linear programming problem: maximize 4+3 subject to 4+3\leq23 5-\leq5 ,\geq0 What is the (Ci- Zi) value for S2 at the initial solution?

________ in linear programming is when a basic variable takes on a value of zero (i.e., a zero in the right-hand side of the constraints of the tableau).

When solving a linear programming problem, a decision variable that leaves the basis in one iteration of the simplex method can return to the basis on a later iteration.

The simplex method does not guarantee an integer solution.

Row operations are used to solve simultaneous equations where equations are multiplied by constants and added or subtracted from each other.

Solve the following problem using the simplex method. Minimize =2+6 Subject to: 2+4\leq12 3+2\geq9 ,\geq0

Given the following linear programming problem: maximize 4+3 subject to 4+3\leq23 5-\leq5 ,\geq0 What is the value of x2 in the final tableau?

Management Science

Linear Programming: Model Formulation and Graphical Solution

Linear Programming: Computer Solution and Sensitivity Analysis

Linear Programming: Modeling Examples

Integer Programming

Transportation, Transshipment, and Assignment Problems

Network Flow Models

Project Management

Multicriteria Decision Making

Nonlinear Programming

Probability and Statistics

Decision Analysis

Queuing Analysis

Simulation

Forecasting

Inventory Management

Transportation and Assignment Solution Methods

Integer Programming: the Branch and Bound Method

Nonlinear Programming: Solution Techniques

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Exam 17: the Simplex Solution Method

The simplex method is a general mathematical solution technique for solving linear programming problems.

The simplex method is a general mathematical solution technique for solving ________ programming problems.

Consider the following linear programming problem and the corresponding final tableau. MAX Z=3+5 s.t. \leq4 2\leq12 3+2\geq18 What is the shadow price for each constraint?

If the primal problem has three constraints, then the corresponding dual problem will have three ________.

Consider the following linear programming problem: MAX =10+30 s.t. 4+6\leq12 8+4\leq16 Use the two tables below to create the initial tableau and perform 1 pivot.

Slack variables are added to constraints and represent unused resources.

Write the dual form of the following linear program. MAX =3+5 s.t. \leq4 2\leq12 3+2\geq18

Artificial variables are added to constraints and represent unused resources.

In solving a linear programming problem with simplex method, the number of basic variables is the same as the number of constraints in the original problem

The ________ step in solving a linear programming model manually with the simplex method is to convert the model into standard form.

Given the following linear programming problem: maximize =\ 100+80 subject to +2\leq40 3+\leq60 ,\geq0 Using the simplex method, what is the optimal value for the objective function?

The leaving variable is determined by dividing the quantity values by the pivot column values and selecting the

The simplex method cannot be used to solve quadratic programming problems.

Given the following linear programming problem: maximize 4+3 subject to 4+3\leq23 5-\leq5 ,\geq0 What is the (Ci- Zi) value for S2 at the initial solution?

________ in linear programming is when a basic variable takes on a value of zero (i.e., a zero in the right-hand side of the constraints of the tableau).

When solving a linear programming problem, a decision variable that leaves the basis in one iteration of the simplex method can return to the basis on a later iteration.

The simplex method does not guarantee an integer solution.

Row operations are used to solve simultaneous equations where equations are multiplied by constants and added or subtracted from each other.

Solve the following problem using the simplex method. Minimize =2+6 Subject to: 2+4\leq12 3+2\geq9 ,\geq0

Given the following linear programming problem: maximize 4+3 subject to 4+3\leq23 5-\leq5 ,\geq0 What is the value of x2 in the final tableau?

Management Science

Linear Programming: Model Formulation and Graphical Solution

Linear Programming: Computer Solution and Sensitivity Analysis

Linear Programming: Modeling Examples

Integer Programming

Transportation, Transshipment, and Assignment Problems

Network Flow Models

Project Management

Multicriteria Decision Making

Nonlinear Programming

Probability and Statistics

Decision Analysis

Queuing Analysis

Simulation

Forecasting

Inventory Management

Transportation and Assignment Solution Methods

Integer Programming: the Branch and Bound Method

Nonlinear Programming: Solution Techniques

Game Theory

Markov Analysis

Filters