Föreläsningar del 4

Question 1

Flashcard 3: Q: What should you do if the problem is a minimization problem when setting up the initial simplex tableau?

Answer 1

A: Multiply the objective function by -1.

Question 2

Flashcard 4: Q: What should you do if the problem formulation contains constraints with negative right-hand sides when setting up the initial simplex tableau?

Answer 2

A: Multiply each constraint by -1.

Question 3

Flashcard 5: Q: What is added to each ≤ constraint when setting up the initial simplex tableau?

Answer 3

A: A slack variable is added.

Question 4

Flashcard 6: Q: What should you subtract and add to each ≥ constraint when setting up the initial simplex tableau?

Answer 4

A: Subtract a surplus variable and add an artificial variable.

Question 5

Flashcard 7: Q: What is set equal to zero in the objective function when setting up the initial simplex tableau?

Answer 5

A: The coefficient of each slack and surplus variable is set to zero.

Question 6

Flashcard 8: Q: What value is set for each artificial variable’s coefficient in the objective function when setting up the initial simplex tableau?

Answer 6

A: Set each artificial variable’s coefficient equal to -M, where M is a very large number.

Question 7

Flashcard 9: Q: What is the first step in the Simplex method?

Answer 7

A: Determine the entering variable by identifying the variable with the most positive value in the cj – zj row.

Question 8

Flashcard 10: Q: How do you determine the leaving variable in the Simplex method?

Answer 8

A: Compute the ratio of the right-hand side values divided by the values in the entering column for each positive entry. Select the variable with the minimal ratio.

Question 9

Flashcard 11: Q: What should you do to generate the next tableau in the Simplex method?

Answer 9

A: Divide the pivot row by the pivot element and update the other rows accordingly using the formula: [new row i] = [current row i] - [aij * row*].

Question 10

Flashcard 12: Q: How do you calculate the cj - zj row in the Simplex method?

Answer 10

A: Multiply the objective function coefficients of the basic variables by the corresponding numbers in the entering column and sum them, then subtract the zj row from the cj row.

Question 11

Flashcard 13: Q: What does it indicate if none of the values in the cj - zj row are positive?

Answer 11

A: It means the problem has been solved, and you can stop.

Question 12

Flashcard 14: Q: What happens if there is an artificial variable in the basis with a positive value in the final tableau?

Answer 12

A: The problem is infeasible, and the simplex method should stop.

Question 13

Flashcard 15: Q: How is infeasibility detected in the simplex method?

Answer 13

A: Infeasibility is detected when an artificial variable remains positive in the final tableau.

Question 14

Flashcard 16: Q: What indicates unboundedness in a linear program (LP)?

Answer 14

A: If all entries in the entering column are non-positive, the LP has an unbounded solution.

Question 15

Flashcard 17: Q: What condition suggests the presence of alternative optimal solutions in an LP?

Answer 15

A: If the final tableau has a cj - zj value equal to 0 for a non-basic variable.

Question 16

Flashcard 18: Q: What is degeneracy in the context of the simplex method?

Answer 16

A: Degeneracy occurs when there is a tie in the ratio test, and an optimal solution may be reached even if some cj - zj values are greater than 0.

Question 17

Flashcard 19: Q: Is the condition cj - zj ≤ 0 sufficient or necessary for optimality in the simplex method?

Answer 17

A: The condition cj - zj ≤ 0 is sufficient for optimality but not necessary.