Deck 6: Linear Programming: The Simplex Method

Question 1

A)
B)
C)
D)

Answer 1

Question 2

Write the e-system obtained via slack variables for the linear programming problem:

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A)
B)
C)
D)

Answer 2

Question 3

Write the e-system obtained via slack variables for the linear programming problem:

-

A)
B)
C)
D)

Answer 3

Question 4

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

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

Question 5

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

A)
B)
C)
D)

Question 6

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

A)
B)
C)
D)

Question 7

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.

A)
B)
C)
D)

Question 8

Refer to the table of the six basic solutions to the e-system:

- Which of the six basic solutions are feasible? Which are not feasible? Use the basic feasible solutions to find the maximum value of

A) Feasible: (A), (B), (E), (F); Not feasible: (C), (D);
The maximum value of P is 246.
B) Feasible: (A), (E), (F); Not feasible: (C), (D), (B);
The maximum value of P is 288.
C) Feasible: (A), (B), (E), (F); Not feasible: (C), (D);
The maximum value of P is 126.
D) Feasible: (A), (B), (E), (F); Not feasible: (C), (D);
The maximum value of P is 288.

Question 9

The following chart depicts basic solutions to a system of linear inequalities. Which of the solutions is NOT feasible?

A) (A), (B), (C)
B) (B) and (E)
C) (B)
D) (A), (D), (E), (F)

Question 10

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:

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A)
B)
C)
D)

Question 11

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:

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A)
B)
C)
D)

Question 12

Graph the system of inequalities:

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A)
B)
C)
D)

Question 13

Graph the system of inequalities:

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A)
B)
C)
D)

Question 14

Solve the given linear programming problem using the table method:

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A)
B)
C)
D)

Question 15

Solve the given linear programming problem using the table method:

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A)
B)
C)
D)

Question 16

A linear programming problem has 4 decision variables, to ,and 8 problem constraints. How many rows are there in the table of basic solutions of the associated e-system?

A) 248
B) 11,880
C) 495
D) 24

Question 17

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?

A)
B)
C)
D)

Question 18

Write the basic solution for the following simplex tableau:

A)
B)
C)
D)

Question 19

Write the basic solution for the following simplex tableau:

A)
B)
C)
D)

Question 20

Write the basic solution for the following simplex tableau:

A)
B)
C)
D)

Question 21

Write the simplex tableau, label the columns and rows for the linear programming problem:

A)
B)
C)
D)

Question 22

Write the simplex tableau, label the columns and rows, underline the pivot element, and identify the entering and exiting variables for the linear programming problem:

A)
B)
C)
D)

Question 23

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:

Question 24

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

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A)
B)
C)
D)

Question 25

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

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A)
B)
C)
D)

Question 26

For the following initial simplex tableau, identify the basic and nonbasic variables. Find the pivot element, the entering and exiting variables, and perform one pivot operation.

Question 27

Pivot once about the circled element in the simplex tableau, and read the solution from the result:

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A)
B)
C)
D)

Question 28

Pivot once about the circled element in the simplex tableau, and read the solution from the result:

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A)
B)
C)
D)

Question 29

Solve the following linear programming problem using the simplex method:

A)
B)
C)
D)

Question 30

Solve the following linear programming problem using the simplex method:

A)
B)
C)
D)

Question 31

Solve the following linear programming problem using the simplex method:

A)
B)
C)
D)

Question 32

Big Round Cheese Company has on hand 45 pounds of Cheddar and 49 pounds of Brie each day. It prepares two Christmas packages-the "Holiday"box, which has 5 pounds of Cheddar and 2 pounds of Brie, and the "Noel"box, which contains 2 pounds of Cheddar and 7 pounds of Brie. Profit on each Holiday assortment is $6, profit on each Noel assortment is $8.
(a) Give the optimal production schedule and the resulting maximum profit.
(b) How much excess Cheddar and excess Brie remain each day if this plan is followed?

Question 33

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.

Question 34

Find the transpose of the matrix:

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A)
B)
C)
D)

Question 35

Find the transpose of the matrix:

-

A)
B)
C)
D)

Question 36

Formulate the dual problem for the linear programming problem:

A)
B)
C)
D)

Question 37

Formulate the dual problem for the linear programming problem:

A)
B)
C)
D)

Question 38

Formulate the dual problem for the linear programming problem:

A)
B)
C)
D)

Question 39

Formulate the dual problem for the linear programming problem:

A)
B)
C)
D)

Question 40

State the dual problem.

A)
B)
C)
D)

Question 41

Formulate the dual problem for the linear programming problem.

A)
B)
C)
D)

Question 42

Consider the following linear programming problem.
Find the optimal solution of the minimization problem.

Question 43

Consider the following linear programming problem.
Find the optimal solution of the minimization problem .

Question 44

Use the simplex method to solve the linear programming problem.

A)
B)
C)
D)

Question 45

Solve the following linear programming problem by applying the simplex method to the dual problem:

A)
B)
C)
D)

Question 46

Solve the linear programming problem by using the simplex method.

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

Question 47

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?

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 48

Write the modified problem for the following linear programming problem (DO NOT SOLVE):

A)
B)
C)
D)

Question 49

Find the initial simplex tableau for the following preliminary simplex tableau (DO NOT SOLVE):

A)
B)
C)
D)

Question 50

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

A)
B)
C)
D)
E)

Question 51

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

A)
B)
C)
D)

Question 52

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

A)
B)
C)
D)

Question 53

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.)

Question 54

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

Question 55

Solve the linear programming problem.

A)
B)
C)
D)

Question 56

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.)

A)
B)
C)
D)

Question 57

A catering company makes three kinds of Jello salad-orange, strawberry, and lemon. It supplies two outlet stores, Outlet A and Outlet B. The company can make up to 14 trays of orange, 20 trays of strawberry, and 24 trays of lemon per day. Outlet A needs at least 20 trays of Jello per day and Outlet B needs at least 10 trays of Jello per day. The transportation costs for shipping trays from the company to the outlets are given in the chart below:
Type of JelloOutlet AOutlet BOrange$4$1Strawberry$1$4Lemon$5$5Formulate a linear programming problem that will determine a shipping schedule that will minimize the cost of transporting the Jello salads to fill the needs of the two outlets. DO NOT SOLVE.

A)
B)
C)
D)

Question 58

A)
B)
C)
D)