MS12-TB18 - Chapter 18 - 1 18 Simplex-Based Sensitivity...

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Chapter 18 - 1 18 Simplex-Based Sensitivity Analysis and Duality MULTIPLE CHOICE 1. Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering a. dual analysis. b. optimality analysis. c. ranging analysis. d. sensitivity analysis. ANSWER: d TOPIC: Sensitivity analysis with the simplex tableau 2. For the basic feasible solution to remain optimal a. all c j - z j values must remain 0. b. no objective function coefficients are allowed to change. c. the value of the objective function must not change. d. each of the above is true. ANSWER: a TOPIC: Objective function coefficients 3. A one-sided range of optimality a. always occurs for non-basic variables. b. always occurs for basic variables. c. indicates changes in more than one coefficient. d. indicates changes in a slack variable’s coefficient. ANSWER: a TOPIC: Objective function coefficients 4. A linear programming problem with the objective function 3x 1 + 8x 2 has the optimal solution x 1 = 5, x 2 = 6. If c 2 decreases by 2 and the range of optimality shows 5 c 2 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. ANSWER: a TOPIC: Objective function coefficients 5. The improvement in the value of the optimal solution per-unit increase in a constraint’s right-hand side is
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Chapter 18 - 2 a. the slack value. b. the dual price. c. never negative. d. the 100% rule. ANSWER: b TOPIC: Right-hand-side values 6. The dual variable represents a. the marginal value of the constraint b. the right-hand-side value of the constraint c. the artificial variable d. the technical coefficient of the constraint ANSWER: a TOPIC: Duality 7. The range of feasibility indicates right-hand-side values for which a. the value of the objective function will not change. b. the values of the decision variables will not change. c. those variables which are in the basis will not change. d. more simplex iterations must be performed. ANSWER: c TOPIC: Right-hand-side values 8. If the dual price for b 1 is 2.7, the range of feasibility is 20 b 1 50, and the original value of b 1 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. ANSWER: d TOPIC: Right-hand-side values 9. The number of constraints to the dual of the following problem is: Max Z = 3x 1 + 2x 2 + 6x 3 s.t. 4x 1 + 2x 2 + 3x 3 100 2x 1 + x 2 - 2x 3 200 4x 2 + x 3 200 a. 1. b. 2. c.
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MS12-TB18 - Chapter 18 - 1 18 Simplex-Based Sensitivity...

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