Question 1

A surplus variable is added to an = constraint in order to utilize the simplex algorithm.

Accepted Answer

A) True 
 B)False

Question 2

List the five steps to form a dual.

Accepted Answer

(1)If the primal is a maximization,the d

Question 3

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 4

Variables in the solution mix are called

Accepted Answer

A) standard. 
B) surplus. 
C) real. 
D) revealed. 
E) basic. 
A) standard. 
B) surplus. 
C) real. 
D) revealed. 
E) basic.

Question 5

The constraint 5 X1 + 6 X2 ≤ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X1 + 6 X2 - S = 30.

Accepted Answer

A) True 
 B)False

Question 6

Explain how an unbounded solution is recognized when calculating the simplex tableaus.

Accepted Answer

if all of the row ra

Question 7

Table M7-1  
-According to Table M7-1,it is currently profitable to produce some units of X1 and the current profit per unit of X1 is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

Accepted Answer

A) 8 
B) 16 
C) 20 
D) 30 
E) None of the above 
A) 8 
B) 16 
C) 20 
D) 30 
E) None of the above

Question 8

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. 
E) None of the above 
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. 
E) None of the above

Question 9

Write the dual of the following linear program:
Minimize Z = 12 X1 + 30 X2
Subject to: 32 X1 + 18 X2 ≥ 600
24 X1 + 48 X2 ≥ 800
X1,X2 ≥ 0

Accepted Answer

Maximize 600U₁ + 800U

Question 10

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. 
E) None of the above 
A) indeterminant. 
B) degenerate. 
C) infeasible. 
D) unbounded. 
E) None of the above

Question 11

Explain how degeneracy is recognized when using the simplex algorithm.

Accepted Answer

when two r

Question 12

Slack and surplus variables are used in simplex only for the solution of maximization problems.

Accepted Answer

A) True 
 B)False

Question 13

The Cj - Zj row of a simplex tableau gives

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. 
E) None of the above 
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. 
E) None of the above

Question 14

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. 
E) None of the above 
A) infeasibility. 
B) unboundedness. 
C) degeneracy. 
D) alternate optimal solutions. 
E) None of the above

Question 15

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) all the artificial variables have a positive value. 
E) None of the above 
A) all slack variables have a zero value. 
B) all basic variables are negative. 
C) all the real variables have a nonzero value. 
D) all the artificial variables have a positive value. 
E) None of the above

Question 16

The dual problem formulation can be solved using the same simplex process used for the primal formulation.

Accepted Answer

A) True 
 B)False

Question 17

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. 
E) None of the above 
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. 
E) None of the above

Question 18

Explain how no feasible solution is recognized when using the simplex algorithm.

Accepted Answer

if an artificial var

Question 19

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. 
E) None of the above 
A) four variables and three constraints. 
B) three variables and four constraints. 
C) four variables and seven constraints. 
D) seven variables and four constraints. 
E) None of the above

Question 20

In linear programs with many variables,even though we cannot graph the feasible region,the optimal solution will still lie at a "corner point."

Accepted Answer

A) True 
 B)False

Exam 22: Linear Programming: The Simplex Method

A surplus variable is added to an = constraint in order to utilize the simplex algorithm.

List the five steps to form a dual.

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?

Variables in the solution mix are called

The constraint 5 X1 + 6 X2 ≤ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X1 + 6 X2 - S = 30.

Explain how an unbounded solution is recognized when calculating the simplex tableaus.

Table M7-1 -According to Table M7-1,it is currently profitable to produce some units of X1 and the current profit per unit of X1 is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

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

Write the dual of the following linear program: Minimize Z = 12 X1 + 30 X2 Subject to: 32 X1 + 18 X2 ≥ 600 24 X1 + 48 X2 ≥ 800 X1,X2 ≥ 0

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:

Explain how degeneracy is recognized when using the simplex algorithm.

Slack and surplus variables are used in simplex only for the solution of maximization problems.

The Cj - Zj row of a simplex tableau gives

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

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

The dual problem formulation can be solved using the same simplex process used for the primal formulation.

The substitution rates give

Explain how no feasible solution is recognized when using the simplex algorithm.

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

In linear programs with many variables,even though we cannot graph the feasible region,the optimal solution will still lie at a "corner point."

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The constraint 5 X₁ + 6 X₂ ≤ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X₁ + 6 X₂ - S = 30.

Table M7-1 -According to Table M7-1,it is currently profitable to produce some units of X₁ and the current profit per unit of X₁ is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

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

Write the dual of the following linear program: Minimize Z = 12 X₁ + 30 X₂ Subject to: 32 X₁ + 18 X₂ ≥ 600 24 X₁ + 48 X₂ ≥ 800 X₁,X₂ ≥ 0

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:

The C_j - Z_j row of a simplex tableau gives

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