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Linear Programming:

Sensitivity Analysis and Interpretation of Solution

MULTIPLE CHOICE

1. To solve a linear programming problem with thousands of variables and constraints

a. a personal computer can be used.

b. a mainframe computer is required.

c. the problem must be partitioned into subparts.

d. unique software would need to be developed.

ANSWER: a

TOPIC: Computer solution

2. A negative dual price for a constraint in a minimization problem means

a. as the right-hand side increases, the objective function value will increase.

b. as the right-hand side decreases, the objective function value will increase.

c. as the right-hand side increases, the objective function value will decrease.

d. as the right-hand side decreases, the objective function value will decrease.

ANSWER: a

TOPIC: Dual price

3. If a decision variable is not positive in the optimal solution, its reduced cost is

a. what its objective function value would need to be before it could become positive.

b. the amount its objective function value would need to improve before it could become positive.

c. zero.

d. its dual price.

ANSWER: b

TOPIC: Reduced cost

4. A constraint with a positive slack value

a. will have a positive dual price.

b. will have a negative dual price.

c. will have a dual price of zero.

d. has no restrictions for its dual price.

ANSWER: c

TOPIC: Slack and dual price

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2Chapter 8 LP Sensitivity Analysis and Interpretation of Solution

5. The amount by which an objective function coefficient can change before a different set of values for the

decision variables becomes optimal is the

a. optimal solution.

b. dual solution.

c. range of optimality.

d. range of feasibility.

ANSWER: c

TOPIC: Range of optimality

6. The range of feasibility measures

a. the right-hand-side values for which the objective function value will not change.

b. the right-hand-side values for which the values of the decision variables will not change.

c. the right-hand-side values for which the dual prices will not change.

d. each of the above is true.

ANSWER: c

TOPIC: Range of feasibility

7. The 100% Rule compares

a. proposed changes to allowed changes.

b. new values to original values.

c. objective function changes to right-hand side changes.

d. dual prices to reduced costs.

ANSWER: a

TOPIC: Simultaneous changes

8. An objective function reflects the relevant cost of labor hours used in production rather than treating them

as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is

a. the maximum premium (say for overtime) over the normal price that the company would be

willing to pay.

b. the upper limit on the total hourly wage the company would pay.

c. the reduction in hours that could be sustained before the solution would change.

d. the number of hours by which the right-hand side can change before there is a change in the

solution point.

ANSWER: a

TOPIC: Dual price

9. A section of output from The Management Scientist is shown here.

Variable Lower Limit Current Value Upper Limit

1 60 100 120

What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

a. Nothing. The values of the decision variables, the dual prices, and the objective function will all

remain the same.

b. The value of the objective function will change, but the values of the decision variables and the

dual prices will remain the same.

c. The same decision variables will be positive, but their values, the objective function value, and

the dual prices will change.

d. The problem will need to be resolved to find the new optimal solution and dual price.

ANSWER: b

TOPIC: Range of optimality

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Chapter 8 LP Sensitivity Analysis and Interpretation of Solution 3

10. A section of output from The Management Scientist is shown here.

Constrain

tLower Limit Current Value Upper Limit

2 240 300 420

What will happen if the right-hand-side for constraint 2 increases by 200?

a. Nothing. The values of the decision variables, the dual prices, and the objective function will all

remain the same.

b. The value of the objective function will change, but the values of the decision variables and the

dual prices will remain the same.

c. The same decision variables will be positive, but their values, the objective function value, and

the dual prices will change.

d. The problem will need to be resolved to find the new optimal solution and dual price.

ANSWER: d

TOPIC: Range of feasibility

11. The amount that the objective function coefficient of a decision variable would have to improve before that

variable would have a positive value in the solution is the

a. dual price.

b. surplus variable.

c. reduced cost.

d. upper limit.

ANSWER: c

TOPIC: Interpretation of computer output

12. The dual price measures, per unit increase in the right hand side,

a. the increase in the value of the optimal solution.

b. the decrease in the value of the optimal solution.

c. the improvement in the value of the optimal solution.

d. the change in the value of the optimal solution.

ANSWER: c

TOPIC: Interpretation of computer output

13. Sensitivity analysis information in computer output is based on the assumption of

a. no coefficient change.

b. one coefficient change.

c. two coefficient change.

d. all coefficients change.

ANSWER: b

TOPIC: Simultaneous changes

14. When the cost of a resource is sunk, then the dual price can be interpreted as the

a. minimum amount the firm should be willing to pay for one additional unit of the resource.

b. maximum amount the firm should be willing to pay for one additional unit of the resource.

c. minimum amount the firm should be willing to pay for multiple additional units of the resource.

d. maximum amount the firm should be willing to pay for multiple additional units of the resource.

ANSWER: b

TOPIC: Dual price

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