Table M7-3 -According to Table M7-3,which is the final simplex tableau for a linear programming problem (maximization),what would happen to profits if the X1 column were selected as the pivot column and another iteration of the simplex algorithm were performed?

A) Total profits would increase. B) Total profits would decrease. C) An infeasible solution would be found. D) Another optimal solution would be found. E) None of the above A) Total profits would increase. B) Total profits would decrease. C) An infeasible solution would be found. D) Another optimal solution would be found. E) None of the above

The number -2 in the X2 column and X1 row of a simplex tableau implies that

A) if 1 unit of X2 is added to the solution,X1 will decrease by 2. B) if 1 unit of X1 is added to the solution,X2 will decrease by 2. C) if 1 unit of X2 is added to the solution,X1 will increase by 2. D) if 1 unit of X1 is added to the solution,X2 will increase by 2. E) None of the above A) if 1 unit of X2 is added to the solution,X1 will decrease by 2. B) if 1 unit of X1 is added to the solution,X2 will decrease by 2. C) if 1 unit of X2 is added to the solution,X1 will increase by 2. D) if 1 unit of X1 is added to the solution,X2 will increase by 2. E) None of the above

Exam 22: Linear Programming: The Simplex Method

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a linear programming problem (maximization),what would happen to profits if the X₁ column were selected as the pivot column and another iteration of the simplex algorithm were performed?

(Multiple Choice)

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Question 41

If,at an optimal solution,the C_j - Z_j value for a real variable that is not in the solution mix has a value of one,there are multiple optimal solutions.

(True/False)

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Question 42

Consider the following general form of a linear programming problem: Maximize Profit Subject to: Amount of resource A used ≤ 100 units Amount of resource B used ≤ 240 units Amount of resource C used ≤ 50 units The shadow price for S₁ is 25,for S₂ is 0,and for S₃ is 40.If the right-hand side of constraint 3 were changed from 150 to 151,what would happen to maximum possible profit?

(Multiple Choice)

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Question 43

In a maximization problem,if a variable is to enter the solution,it must have a positive coefficient in the C_j - Z_j row.

(True/False)

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Question 44

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

(Multiple Choice)

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Question 45

Solve the following linear programming problem using the simplex method. Maximize 3 X₁ + 5X₂ Subject to: 4 X₁ + 3 X₂ ≤ 48 X₁ + 2 X₂ ≤ 20 X₁,X₂ ≥ 0

(Essay)

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Question 46

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

(Multiple Choice)

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Question 47

Sensitivity testing of basic variables involves reworking the initial simplex tableau.

(True/False)

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Question 48

The solution to the dual LP problem

(Multiple Choice)

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Question 49

Consider the following linear program: Maximize Z = 3 X₁ + 2 X₂ - X₃ Subject to: X₁+ X₂ + 2 X₃ ≤ 10 2 X₁ - X₂ + X₃ ≤ 20 3 X₁ + X₂ ≤ 15 X₁,X₂,X₃ ≥ 0 (a)Convert the above constraints to equalities by adding the appropriate slack variables. (b)Set up the initial simplex tableau and solve.

(Essay)

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Question 50

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

(True/False)

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Question 51

Sensitivity analyses are used to examine the effects of changes in

(Multiple Choice)

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Question 52

In linear programs with more than two decision variables,the area of feasible solutions is represented by an n-dimensional polyhedron.

(True/False)

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Question 53

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

(Essay)

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Question 54

An artificial variable has no physical interpretation but

(Multiple Choice)

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Question 55

The number -2 in the X₂ column and X₁ row of a simplex tableau implies that

(Multiple Choice)

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Question 56

The substitution rates

(Multiple Choice)

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Question 57

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.

(True/False)

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Question 58

The dual of a linear programming problem

(Multiple Choice)

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Question 59

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?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 100

Exam 22: Linear Programming: The Simplex Method

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a linear programming problem (maximization),what would happen to profits if the X1 column were selected as the pivot column and another iteration of the simplex algorithm were performed?

If,at an optimal solution,the Cj - Zj value for a real variable that is not in the solution mix has a value of one,there are multiple optimal solutions.

In a maximization problem,if a variable is to enter the solution,it must have a positive coefficient in the Cj - Zj row.

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

Solve the following linear programming problem using the simplex method. Maximize 3 X1 + 5X2 Subject to: 4 X1 + 3 X2 ≤ 48 X1 + 2 X2 ≤ 20 X1,X2 ≥ 0

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

Sensitivity testing of basic variables involves reworking the initial simplex tableau.

The solution to the dual LP problem

Consider the following linear program: Maximize Z = 3 X1 + 2 X2 - X3 Subject to: X1+ X2 + 2 X3 ≤ 10 2 X1 - X2 + X3 ≤ 20 3 X1 + X2 ≤ 15 X1,X2,X3 ≥ 0 (a)Convert the above constraints to equalities by adding the appropriate slack variables. (b)Set up the initial simplex tableau and solve.

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

Sensitivity analyses are used to examine the effects of changes in

In linear programs with more than two decision variables,the area of feasible solutions is represented by an n-dimensional polyhedron.

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

An artificial variable has no physical interpretation but

The number -2 in the X2 column and X1 row of a simplex tableau implies that

The substitution rates

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.

The dual of a linear programming problem

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?

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Table M7-3 -According to Table M7-3,which is the final simplex tableau for a linear programming problem (maximization),what would happen to profits if the X₁ column were selected as the pivot column and another iteration of the simplex algorithm were performed?

If,at an optimal solution,the C_j - Z_j value for a real variable that is not in the solution mix has a value of one,there are multiple optimal solutions.

In a maximization problem,if a variable is to enter the solution,it must have a positive coefficient in the C_j - Z_j row.

Solve the following linear programming problem using the simplex method. Maximize 3 X₁ + 5X₂ Subject to: 4 X₁ + 3 X₂ ≤ 48 X₁ + 2 X₂ ≤ 20 X₁,X₂ ≥ 0

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

The number -2 in the X₂ column and X₁ row of a simplex tableau implies that

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.