The number of constraints to the dual of the following problem is: Max Z = 3x1 + 2x2 + 6x3 S.t.4x1 + 2x2 + 3x3 $\geq$ 100 2x1 + x2 - 2x3 $\leq$ 200 4x2 + x3 $\geq$ 200

A) 1. B) 2. C) 3. D) 4. A) 1. B) 2. C) 3. D) 4.

If the dual price for b1 is 2.7, the range of feasibility is 20 $\leq$ b1 $\leq$ 50, and the original value of b1 was 30, which of the following is true?

A) There currently is no slack in the first constraint. B) We would be willing to pay up to $2.70 per unit for up to 20 more units of resource 1. C) If only 25 units of resource 1 were available, profit would drop by $13.50. D) Each of the above is true. A) There currently is no slack in the first constraint. B) We would be willing to pay up to $2.70 per unit for up to 20 more units of resource 1. C) If only 25 units of resource 1 were available, profit would drop by $13.50. D) Each of the above is true.

A linear programming problem with the objective function 3x1 + 8x2 has the optimal solution x1 = 5, x2 = 6.If c2 decreases by 2 and the range of optimality shows 5 $\leq$ c2 $\leq$ 12, the value of Z

A) will decrease by 12. B) will decrease by 2. C) will not change. D) cannot be determined from this information. A) will decrease by 12. B) will decrease by 2. C) will not change. D) cannot be determined from this information.

Exam 18: Simplex-Based Sensitivity Analysis and Duality

The entries in the associated slack column of the final tableau indicate the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.

Free

(True/False)

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Question 1

Correct Answer:

Verified

True

The improvement in the value of the optimal solution per-unit increase in a constraint's right-hand side is

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

The ranges for which the right-hand-side values are valid are the same as the ranges over which the dual prices are valid.

Free

(True/False)

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Question 3

Correct Answer:

Verified

True

The dual variable represents

(Multiple Choice)

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Question 4

As long as the objective function coefficient remains within the range of optimality, the variable values will not change although the value of the objective function could.

(True/False)

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Question 5

The dual price is the improvement in value of the optimal solution per unit increase in the value of the right-hand-side associated with a linear programming problem.

(True/False)

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Question 6

The range of optimality is calculated by considering changes in the c_j - z_j value of the variable in question.

(True/False)

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Question 7

The number of constraints to the dual of the following problem is: Max Z = 3x₁ + 2x₂+ 6x₃ S.t.4x₁ + 2x₂ + 3x₃ $\geq$ 100 2x₁ + x₂ - 2x₃ $\leq$ 200 4x₂ + x₃ $\geq$ 200

(Multiple Choice)

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Question 8

The dual price for an equality constraint is the z_j value for its artificial variable.

(True/False)

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Question 9

Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering

(Multiple Choice)

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Question 10

There is a dual price associated with each decision variable.

(True/False)

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Question 11

If the simplex tableau is from a maximization converted from a minimization, the signs and directions of the inequalities that give the objective function ranges will need to be adjusted to apply to the original coefficients.

(True/False)

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Question 12

The range of feasibility indicates right-hand-side values for which

(Multiple Choice)

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Question 13

The range of optimality is useful only for basic variables.

(True/False)

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Question 14

If the dual price for b₁ is 2.7, the range of feasibility is 20 $\leq$ b₁ $\leq$ 50, and the original value of b₁ was 30, which of the following is true?

(Multiple Choice)

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Question 15

For the basic feasible solution to remain optimal

(Multiple Choice)

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Question 16

A linear programming problem with the objective function 3x₁ + 8x₂ has the optimal solution x₁ = 5, x₂ = 6.If c₂ decreases by 2 and the range of optimality shows 5 $\leq$ c₂ $\leq$ 12, the value of Z

(Multiple Choice)

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Question 17

Given the simplex tableau for the optimal primal solution

(Multiple Choice)

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Question 18

A one-sided range of optimality

(Multiple Choice)

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Question 19

The range of optimality for a basic variable defines the objective function coefficient values for which the variable will remain part of the current optimal basic feasible solution.

(True/False)

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Question 20

Showing 1 - 20 of 20

Exam 18: Simplex-Based Sensitivity Analysis and Duality

The entries in the associated slack column of the final tableau indicate the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.

The improvement in the value of the optimal solution per-unit increase in a constraint's right-hand side is

The ranges for which the right-hand-side values are valid are the same as the ranges over which the dual prices are valid.

The dual variable represents

As long as the objective function coefficient remains within the range of optimality, the variable values will not change although the value of the objective function could.

The dual price is the improvement in value of the optimal solution per unit increase in the value of the right-hand-side associated with a linear programming problem.

The range of optimality is calculated by considering changes in the cj - zj value of the variable in question.

The number of constraints to the dual of the following problem is: Max Z = 3x1 + 2x2 + 6x3 S.t.4x1 + 2x2 + 3x3 ≥\geq≥ 100 2x1 + x2 - 2x3 ≤\leq≤ 200 4x2 + x3 ≥\geq≥ 200

The dual price for an equality constraint is the zj value for its artificial variable.

Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering

There is a dual price associated with each decision variable.

If the simplex tableau is from a maximization converted from a minimization, the signs and directions of the inequalities that give the objective function ranges will need to be adjusted to apply to the original coefficients.

The range of feasibility indicates right-hand-side values for which

The range of optimality is useful only for basic variables.

If the dual price for b1 is 2.7, the range of feasibility is 20 ≤\leq≤ b1 ≤\leq≤ 50, and the original value of b1 was 30, which of the following is true?

For the basic feasible solution to remain optimal

A linear programming problem with the objective function 3x1 + 8x2 has the optimal solution x1 = 5, x2 = 6.If c2 decreases by 2 and the range of optimality shows 5 ≤\leq≤ c2 ≤\leq≤ 12, the value of Z

Given the simplex tableau for the optimal primal solution

A one-sided range of optimality

The range of optimality for a basic variable defines the objective function coefficient values for which the variable will remain part of the current optimal basic feasible solution.

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LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

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The range of optimality is calculated by considering changes in the c_j - z_j value of the variable in question.

The number of constraints to the dual of the following problem is: Max Z = 3x₁ + 2x₂+ 6x₃ S.t.4x₁ + 2x₂ + 3x₃ $\geq$ 100 2x₁ + x₂ - 2x₃ $\leq$ 200 4x₂ + x₃ $\geq$ 200

The dual price for an equality constraint is the z_j value for its artificial variable.

If the dual price for b₁ is 2.7, the range of feasibility is 20 $\leq$ b₁ $\leq$ 50, and the original value of b₁ was 30, which of the following is true?

A linear programming problem with the objective function 3x₁ + 8x₂ has the optimal solution x₁ = 5, x₂ = 6.If c₂ decreases by 2 and the range of optimality shows 5 $\leq$ c₂ $\leq$ 12, the value of Z