Question 1

As we are doing the ratio calculations for a simplex iteration, if there is a tie for the smallest ratio, the problem is degenerate.

Accepted Answer

A) True 
 B)False

Question 2

Dual variables represent the potential value of resources.

Accepted Answer

A) True 
 B)False

Question 3

A slack variable

Accepted Answer

A) is added to each ≤ constraint to facilitate the simplex process. 
B) is added to each ≥ constraint to facilitate the simplex process. 
C) is added to each ≤ or = constraint to facilitate the simplex process. 
D) is added to each = constraint to facilitate the simplex process. 
A) is added to each ≤ constraint to facilitate the simplex process. 
B) is added to each ≥ constraint to facilitate the simplex process. 
C) is added to each ≤ or = constraint to facilitate the simplex process. 
D) is added to each = constraint to facilitate the simplex process.

Question 4

A correctly formulated linear program, when solved with the simplex algorithm, will always yield a single optimal solution.

Accepted Answer

A) True 
 B)False

Question 5

Which of the following is not true about slack variables in a simplex tableau?

Accepted Answer

A) They are used to convert ≤ constraint inequalities to equations. 
B) They represent unused resources. 
C) They require the addition of an artificial variable. 
D) They may represent machine time, labor hours, or warehouse space. 
A) They are used to convert ≤ constraint inequalities to equations. 
B) They represent unused resources. 
C) They require the addition of an artificial variable. 
D) They may represent machine time, labor hours, or warehouse space.

Question 6

In applying the simplex solution procedure to a maximization problem to determine which variable enters the solution mix

Accepted Answer

A) pick the one with the largest positive Cj - Zj. 
B) pick the one with the smallest Cj - Zj. 
C) pick the one with the largest Cj. 
D) pick the one with the smallest Zj. 
A) pick the one with the largest positive Cj - Zj. 
B) pick the one with the smallest Cj - Zj. 
C) pick the one with the largest Cj. 
D) pick the one with the smallest Zj.

Question 7

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

Accepted Answer

if all of the row ra

Question 8

Karmarkar's algorithm is especially useful in solving very large-scale LP problems.

Accepted Answer

A) True 
 B)False

Question 9

How should the constraint, 5X - 2Y ≥ 6, be converted into simplex tableau form?

Accepted Answer

A) 5X - 2Y + S + A = 6 
B) 5X - 2Y - S + A = 6 
C) 5X - 2Y - S = 6 
D) 5X - 2Y + A = 6 
A) 5X - 2Y + S + A = 6 
B) 5X - 2Y - S + A = 6 
C) 5X - 2Y - S = 6 
D) 5X - 2Y + A = 6

Question 10

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

Accepted Answer

if an artificial var

Question 11

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. 
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 12

We can solve a minimization problem by maximizing the negative of the minimization problem's objective function.

Accepted Answer

A) True 
 B)False

Question 13

Table M7-2  
-According to Table M7-2, which is a summarized solution output from simplex analysis, if the amount of resource A were decreased so that there were only 550 units available instead of 600, what would happen to total profits?

Accepted Answer

A) They would decrease. 
B) They would increase. 
C) They would not change. 
D) Unable to determine from the given information. 
A) They would decrease. 
B) They would increase. 
C) They would not change. 
D) Unable to determine from the given information.

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

In solving a linear programming minimization problem using the simplex method

Accepted Answer

A) every time an artificial variable is added, a surplus variable must be subtracted. 
B) every time a surplus variable is added, an artificial variable must be added. 
C) every time a surplus variable is added, an artificial variable must be subtracted. 
D) every time a surplus variable is subtracted, an artificial variable must be added. 
A) every time an artificial variable is added, a surplus variable must be subtracted. 
B) every time a surplus variable is added, an artificial variable must be added. 
C) every time a surplus variable is added, an artificial variable must be subtracted. 
D) every time a surplus variable is subtracted, an artificial variable must be added.

Question 16

The shadow price is the value of one additional unit of a scarce resource across the range (-∞,∞).

Accepted Answer

A) True 
 B)False

Question 17

If one changes a nonbasic objective function coefficient, the optimal solution of a maximization problem will remain optimal if

Accepted Answer

A) the increase in the coefficient does not exceed the value of the Zj associated with that nonbasic variable. 
B) the increase in the coefficient does not exceed the values of the Zj's of every basic variable. 
C) the decrease in the coefficient does not exceed the value of the Zj associated with the nonbasic variable. 
D) the new Cj - Zj associated with the nonbasic variable remains positive. 
A) the increase in the coefficient does not exceed the value of the Zj associated with that nonbasic variable. 
B) the increase in the coefficient does not exceed the values of the Zj's of every basic variable. 
C) the decrease in the coefficient does not exceed the value of the Zj associated with the nonbasic variable. 
D) the new Cj - Zj associated with the nonbasic variable remains positive.

Question 18

Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3
Subject to: X1 + X2 + X3 ≥ 90
12 X1 + 8 X2 + 10 X3 ≤ 1500
X1 , X2 , X3 ≥ 0
How many slack, surplus, and artificial variables would be necessary if the simplex were used to solve this problem?

Accepted Answer

A) 3 slack, 3 surplus, and 3 artificial 
B) 1 slack, 2 surplus, and 2 artificial 
C) 1 slack, 4 surplus, and 4 artificial 
D) 1 slack, 1 surplus, and 1 artificial 
A) 3 slack, 3 surplus, and 3 artificial 
B) 1 slack, 2 surplus, and 2 artificial 
C) 1 slack, 4 surplus, and 4 artificial 
D) 1 slack, 1 surplus, and 1 artificial

Question 19

Convert the following linear program into the simplex form.
Minimize 3x1 + 2x2
Subject to: 7x1 - 2x2 0
5x1 + x2 10
x1 + 7x2 12
3x1 + 3x2 = 16
x1, x2 ≥ 0

Accepted Answer

Minimize 3x1 + 2x2 + 0S1 + 0S2 + 0S3 + M

Question 20

How should the constraint, 5X - 2Y = 6, be converted into simplex tableau form?

Accepted Answer

A) 5X - 2Y + A = 6 
B) 5X - 2Y - A = 6 
C) 5X - 2Y + A1 - A2 = 6 
D) 5X - 2Y + S = 6 
A) 5X - 2Y + A = 6 
B) 5X - 2Y - A = 6 
C) 5X - 2Y + A1 - A2 = 6 
D) 5X - 2Y + S = 6

Exam 22: Linear Programming: The Simplex Method

As we are doing the ratio calculations for a simplex iteration, if there is a tie for the smallest ratio, the problem is degenerate.

Dual variables represent the potential value of resources.

A slack variable

A correctly formulated linear program, when solved with the simplex algorithm, will always yield a single optimal solution.

Which of the following is not true about slack variables in a simplex tableau?

In applying the simplex solution procedure to a maximization problem to determine which variable enters the solution mix

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

Karmarkar's algorithm is especially useful in solving very large-scale LP problems.

How should the constraint, 5X - 2Y ≥ 6, be converted into simplex tableau form?

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

The Cj - Zj row of a simplex tableau gives

We can solve a minimization problem by maximizing the negative of the minimization problem's objective function.

Table M7-2 -According to Table M7-2, which is a summarized solution output from simplex analysis, if the amount of resource A were decreased so that there were only 550 units available instead of 600, what would happen to total profits?

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

In solving a linear programming minimization problem using the simplex method

The shadow price is the value of one additional unit of a scarce resource across the range (-∞,∞).

If one changes a nonbasic objective function coefficient, the optimal solution of a maximization problem will remain optimal if

Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3 Subject to: X1 + X2 + X3 ≥ 90 12 X1 + 8 X2 + 10 X3 ≤ 1500 X1 , X2 , X3 ≥ 0 How many slack, surplus, and artificial variables would be necessary if the simplex were used to solve this problem?

Convert the following linear program into the simplex form. Minimize 3x1 + 2x2 Subject to: 7x1 - 2x2 0 5x1 + x2 10 x1 + 7x2 12 3x1 + 3x2 = 16 x1, x2 ≥ 0

How should the constraint, 5X - 2Y = 6, be converted into simplex tableau form?

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

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Integer Programming, Goal Programming, and Nonlinear Programming

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Filters

The C_j - Z_j row of a simplex tableau gives

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