Question 1

Use the simplex method to solve the linear programming problem.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

Solve the linear programming problem by using the simplex method.

Accepted Answer

A)  x = 0, y = 11, f = 33 
B)    
C)  x = 5, y = 0, f = 25 
D)  x = 5, y = 1, f = 28 
A)  x = 0, y = 11, f = 33 
B)    
C)  x = 5, y = 0, f = 25 
D)  x = 5, y = 1, f = 28

Question 3

Solve the following linear programming problem using the simplex method:

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

A stereo manufacturer makes three types of stereo systems, I, II, and III, with profits of $20, $30, and $40, respectively. No more than 100 type-I systems can be made per day. Type-I systems require 5 man-hours, and the corresponding numbers of man-hours for types II and III are 10 and 15, respectively. If the manufacturer has available 2000 man-hours per day, determine the number of units from each system that must be manufactured in order to maximize profit. Compute the corresponding profit.

Accepted Answer

100 of type-I, 150 o

Question 5

Solve the linear programming problem.

Accepted Answer

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D)    
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B)    
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D)

Question 6

A linear programming problem has 35 decision variables   , ...,   and 50 problem constraints. How many rows are there in the table of basic solutions of the associated e-system?

Accepted Answer

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B)    
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D)    
A)    
B)    
C)    
D)

Question 7

Find the transpose of the matrix:
-

Accepted Answer

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B)    
C)    
D)    
A)    
B)    
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D)

Question 8

Write the basic solution for the following simplex tableau:

Accepted Answer

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B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Find the transpose of the matrix:
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Formulate the following problem as a linear programming problem (DO NOT SOLVE):A shoe company is introducing a new line of running shoes. The marketing division decides to promote the line in a particular city. The promotion will consist of newspaper, radio, and television ads. Each newspaper ad will cost $120, each television ad will cost $370, and each radio ad will cost $210. The company wants to spend at most half their money on newspaper ads. The marketing division believes that each newspaper ad will reach 4,700 men and 3,700 women, each television ad will reach 7,600 men and 6,600 women, and each radio ad will reach 4,500 men and 5,500 women. The promotion will be considered successful if it reaches at least 400,000 men and 200,000 women. How should the company divide its money between the newspaper, television, and radio ads so as to insure a successful promotion at a minimum cost? (Let   equal the number of newspaper ads,   equal the number of television ads, and   equal the number of radio ads purchased in the promotion.)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Refer to the table of the six basic solutions to the e-system:
-    In basic solution (B), identify the basic and nonbasic variables and determine if the solution is feasible or not feasible.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

How many slack variables must be introduced to form the system of problem constraint equations?

Accepted Answer

A)  0 
B)  3 
C)  2 
D)  1 
A)  0 
B)  3 
C)  2 
D)  1

Question 13

State whether the optimal solution has been found, an additional pivot is required, or there is no solution for the problem corresponding to the following simplex tableau:

Accepted Answer

Optimal so

Question 14

Convert the given i-system to an e-system using slack variables. Then construct a table of all basic solutions of the e-system. For each basic solution, indicated whether or not it is feasible:
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Introduce slack variables as necessary, and write the initial simplex tableau for the problem:
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Use the big M method to solve the following linear programming problem.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?

Accepted Answer

A)  12 counselors and 18 aides 
B)  35 counselors and 10 aides 
C)  27 counselors and 18 aides 
D)  18 counselors and 12 aides 
A)  12 counselors and 18 aides 
B)  35 counselors and 10 aides 
C)  27 counselors and 18 aides 
D)  18 counselors and 12 aides

Question 18

Use the big M method to find the optimal solution to the problem.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

Convert the inequality to a linear equation by adding a slack variable.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 20

Consider the linear programming problem:
   (A) Introduce slack, surplus, and artificial variables and form the modified problem. 
(B) Write the preliminary simplex tableau for the modified problem. (DO NOT SOLVE.)

Accepted Answer

The answer of Consider the linear programming problem:
  ...

Use the simplex method to solve the linear programming problem.

Solve the linear programming problem by using the simplex method.

Solve the following linear programming problem using the simplex method:

Solve the linear programming problem.

A linear programming problem has 35 decision variables , ..., and 50 problem constraints. How many rows are there in the table of basic solutions of the associated e-system?

Find the transpose of the matrix: -

Write the basic solution for the following simplex tableau:

Find the transpose of the matrix: -

Refer to the table of the six basic solutions to the e-system: - In basic solution (B), identify the basic and nonbasic variables and determine if the solution is feasible or not feasible.

How many slack variables must be introduced to form the system of problem constraint equations?

State whether the optimal solution has been found, an additional pivot is required, or there is no solution for the problem corresponding to the following simplex tableau:

Convert the given i-system to an e-system using slack variables. Then construct a table of all basic solutions of the e-system. For each basic solution, indicated whether or not it is feasible: -

Introduce slack variables as necessary, and write the initial simplex tableau for the problem: -

Use the big M method to solve the following linear programming problem.

Use the big M method to find the optimal solution to the problem.

Convert the inequality to a linear equation by adding a slack variable.

Consider the linear programming problem: (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem. (DO NOT SOLVE.)

Linear Equations and Graphs

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations; Matrices

Linear Inequalities and Linear Programming

Logic, Sets, and Counting

Probability

Markov Chains

Data Description and Probability Distributions

Games and Decisions

Appendix A: Basic Algebra Review

Appendix B: Special Topics

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Exam 6: Linear Programming: The Simplex Method

Use the simplex method to solve the linear programming problem.

Solve the linear programming problem by using the simplex method.

Solve the following linear programming problem using the simplex method:

Solve the linear programming problem.

A linear programming problem has 35 decision variables , ..., and 50 problem constraints. How many rows are there in the table of basic solutions of the associated e-system?

Find the transpose of the matrix: -

Write the basic solution for the following simplex tableau:

Find the transpose of the matrix: -

Refer to the table of the six basic solutions to the e-system: - In basic solution (B), identify the basic and nonbasic variables and determine if the solution is feasible or not feasible.

How many slack variables must be introduced to form the system of problem constraint equations?

State whether the optimal solution has been found, an additional pivot is required, or there is no solution for the problem corresponding to the following simplex tableau:

Convert the given i-system to an e-system using slack variables. Then construct a table of all basic solutions of the e-system. For each basic solution, indicated whether or not it is feasible: -

Introduce slack variables as necessary, and write the initial simplex tableau for the problem: -

Use the big M method to solve the following linear programming problem.

Use the big M method to find the optimal solution to the problem.

Convert the inequality to a linear equation by adding a slack variable.

Consider the linear programming problem: (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem. (DO NOT SOLVE.)

Linear Equations and Graphs

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations; Matrices

Linear Inequalities and Linear Programming

Logic, Sets, and Counting

Probability

Markov Chains

Data Description and Probability Distributions

Games and Decisions

Appendix A: Basic Algebra Review

Appendix B: Special Topics

Filters