Question 1

In a maximization problem, the Cj - Zj row gives the net loss from introducing one unit of each variable into the solution.

Accepted Answer

A) True 
 B)False

Question 2

Using the simplex method, we know we have an optimal solution when

Accepted Answer

A) all slack variables have a zero value. 
B) all basic variables are negative. 
C) all the real variables have a nonzero value. 
D) the Cj - Zj row has no positive values. 
A) all slack variables have a zero value. 
B) all basic variables are negative. 
C) all the real variables have a nonzero value. 
D) the Cj - Zj row has no positive values.

Question 3

In 1984, who developed an alternative to the simplex algorithm, which often takes significantly less computer time to solve very large-scale LP problems?

Accepted Answer

A) Carmichael 
B) Kruskev 
C) Karmarkar 
D) Krakov 
A) Carmichael 
B) Kruskev 
C) Karmarkar 
D) Krakov

Question 4

Artificial variables can be used in both maximization and minimization problems but are most often used in minimization problems.

Accepted Answer

A) True 
 B)False

Question 5

A simplex formulation that suffers from degeneracy means that the problem has no optimal solution.

Accepted Answer

A) True 
 B)False

Question 6

In the simplex process, the new pivot row is found by dividing each number in the row by the pivot number.

Accepted Answer

A) True 
 B)False

Question 7

The substitution rates give

Accepted Answer

A) the number of units of each basic variable that must be removed from the solution if a new variable is entered. 
B) the gross profit or loss given up by adding one unit of a variable into the solution. 
C) the net profit or loss that will result from introducing one unit of the variable indicated in that column into the solution. 
D) the maximal value a variable can take on and still have all the constraints satisfied. 
A) the number of units of each basic variable that must be removed from the solution if a new variable is entered. 
B) the gross profit or loss given up by adding one unit of a variable into the solution. 
C) the net profit or loss that will result from introducing one unit of the variable indicated in that column into the solution. 
D) the maximal value a variable can take on and still have all the constraints satisfied.

Question 8

If, in the final optimal simplex tableau, the Cj - Zj value for a nonbasic variable is zero, this implies

Accepted Answer

A) infeasibility. 
B) unboundedness. 
C) degeneracy. 
D) alternate optimal solutions. 
A) infeasibility. 
B) unboundedness. 
C) degeneracy. 
D) alternate optimal solutions.

Question 9

Because slack variables yield no profit, they are not included in the objective function when creating the initial simplex tableau.

Accepted Answer

A) True 
 B)False

Question 10

The substitution rates in the slack variable column can be used to determine the actual values of the solution mix variables if the right-hand side of a constraint is changed.What is the relationship that is used to find those values?

Accepted Answer

New quantity = Origi

Question 11

If, in the optimal tableau of a linear programming problem, an artificial variable is present in the solution mix, this implies

Accepted Answer

A) infeasibility. 
B) unboundedness. 
C) degeneracy. 
D) alternate optimal solutions. 
A) infeasibility. 
B) unboundedness. 
C) degeneracy. 
D) alternate optimal solutions.

Question 12

Table M7-3  
-According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what can be said about the optimal solution and the constraints?

Accepted Answer

A) There is slack remaining in the first constraint. 
B) There is slack remaining in the second constraint. 
C) There is slack remaining in both constraints. 
D) There is no slack remaining in either constraint. 
A) There is slack remaining in the first constraint. 
B) There is slack remaining in the second constraint. 
C) There is slack remaining in both constraints. 
D) There is no slack remaining in either constraint.

Question 13

Upon retirement, Mr.Klaws started to make two types of children's wooden toys in his shop.Wuns yield a variable profit of $8 each, and Toos have a contribution margin of $9 each.Even though his electric saw overheats, he can make 7 Wuns or 14 Toos each day.Since he doesn't have equipment for drying the lacquer finish he puts on the toys, the drying operation limits him to 16 Wuns or 8 Toos per day.The final tableau for Mr.Klaws' problem would be:   (a)What would the value be of an additional unit of constraint #1?
(b)What would the value be of an additional unit of constraint #2?

Accepted Answer

The answer of Upon retirement, Mr.Klaws started to make two...

Question 14

For a maximization problem, the Zj values in the body of the simplex table represent the gross profit given up by adding one unit of this variable into the current solution.

Accepted Answer

A) True 
 B)False

Question 15

For every primal

Accepted Answer

A) that is a maximization problem, the dual is also a maximization problem. 
B) the right-hand side quantities become the dual's objective function right-hand side. 
C) constraint inequality signs are the same as in the dual. 
D) the transpose of the constraint coefficients become the dual's constraint coefficients. 
A) that is a maximization problem, the dual is also a maximization problem. 
B) the right-hand side quantities become the dual's objective function right-hand side. 
C) constraint inequality signs are the same as in the dual. 
D) the transpose of the constraint coefficients become the dual's constraint coefficients.

Question 16

How does Karmarkar's Algorithm differ from the simplex method?

Accepted Answer

A) It follows a path of integer solutions. 
B) It follows a path inside the feasible region. 
C) It follows a counterclockwise path around the outside edges of the feasible region. 
D) It follows a clockwise path around the outside edges of the feasible region. 
A) It follows a path of integer solutions. 
B) It follows a path inside the feasible region. 
C) It follows a counterclockwise path around the outside edges of the feasible region. 
D) It follows a clockwise path around the outside edges of the feasible region.

Question 17

Write the dual of the following linear program.
Maximize 3 X1 + 5X2
Subject to: 4 X1 + 2 X2 ≤ 44
X1 + 2 X2 ≤ 24
X1, X2 ≥ 0

Accepted Answer

Minimize 44U1 + 24U2

Question 18

A primal linear programming problem has four variables and three constraints.The dual of this will have

Accepted Answer

A) four variables and three constraints. 
B) three variables and four constraints. 
C) four variables and seven constraints. 
D) seven variables and four constraints. 
A) four variables and three constraints. 
B) three variables and four constraints. 
C) four variables and seven constraints. 
D) seven variables and four constraints.

Question 19

A solved LP problem indicated that the optimal solution was X1 = 5, X2 = 10, A1 = 40.The first constraint was: 4X1 + 2X2 ≥ 80.This solution is

Accepted Answer

A) indeterminant. 
B) degenerate. 
C) infeasible. 
D) unbounded. 
A) indeterminant. 
B) degenerate. 
C) infeasible. 
D) unbounded.

Question 20

Table M7-3  
-According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, the 0.667 in the X1 column means that

Accepted Answer

A) to produce 1 unit of X1, 0.667 units of X2 must be given up. 
B) to produce 1 unit of X2, 0.667 units of X1 must be given up. 
C) if 1 unit of X1 is produced, profits on X2 will decrease by 0.667. 
D) if 1 unit of X1 is produced, profits on X2 will increase by 0.667. 
A) to produce 1 unit of X1, 0.667 units of X2 must be given up. 
B) to produce 1 unit of X2, 0.667 units of X1 must be given up. 
C) if 1 unit of X1 is produced, profits on X2 will decrease by 0.667. 
D) if 1 unit of X1 is produced, profits on X2 will increase by 0.667.

Exam 22: Linear Programming: The Simplex Method

In a maximization problem, the Cj - Zj row gives the net loss from introducing one unit of each variable into the solution.

Using the simplex method, we know we have an optimal solution when

In 1984, who developed an alternative to the simplex algorithm, which often takes significantly less computer time to solve very large-scale LP problems?

Artificial variables can be used in both maximization and minimization problems but are most often used in minimization problems.

A simplex formulation that suffers from degeneracy means that the problem has no optimal solution.

In the simplex process, the new pivot row is found by dividing each number in the row by the pivot number.

The substitution rates give

If, in the final optimal simplex tableau, the Cj - Zj value for a nonbasic variable is zero, this implies

Because slack variables yield no profit, they are not included in the objective function when creating the initial simplex tableau.

The substitution rates in the slack variable column can be used to determine the actual values of the solution mix variables if the right-hand side of a constraint is changed.What is the relationship that is used to find those values?

If, in the optimal tableau of a linear programming problem, an artificial variable is present in the solution mix, this implies

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what can be said about the optimal solution and the constraints?

For a maximization problem, the Zj values in the body of the simplex table represent the gross profit given up by adding one unit of this variable into the current solution.

For every primal

How does Karmarkar's Algorithm differ from the simplex method?

Write the dual of the following linear program. Maximize 3 X1 + 5X2 Subject to: 4 X1 + 2 X2 ≤ 44 X1 + 2 X2 ≤ 24 X1, X2 ≥ 0

A primal linear programming problem has four variables and three constraints.The dual of this will have

A solved LP problem indicated that the optimal solution was X1 = 5, X2 = 10, A1 = 40.The first constraint was: 4X1 + 2X2 ≥ 80.This solution is

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, the 0.667 in the X1 column means that

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In a maximization problem, the C_j - Z_j row gives the net loss from introducing one unit of each variable into the solution.

If, in the final optimal simplex tableau, the C_j - Z_j value for a nonbasic variable is zero, this implies

For a maximization problem, the Z_j values in the body of the simplex table represent the gross profit given up by adding one unit of this variable into the current solution.

A solved LP problem indicated that the optimal solution was X₁ = 5, X₂ = 10, A₁ = 40.The first constraint was: 4X₁ + 2X₂ ≥ 80.This solution is

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, the 0.667 in the X₁ column means that