Deck 3: LP Sensitivity Analysis and Interpretation of Solution

Question 1

Output from a computer package is precise and answers should never be rounded.

Answer 1

False

Question 2

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 2

C

Question 3

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 3

C

Question 4

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

Question 5

The reduced cost for a positive decision variable is 0.

Question 6

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.

Question 7

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

Question 8

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.

Question 9

Which of the following is not a question answered by sensitivity analysis?

A)If the right-hand side value of a constraint changes, will the objective function value change?
B)Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing?
C)By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
D)By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?

Question 10

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.

Question 11

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.

Question 12

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.

Question 13

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.

Question 14

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.

Question 15

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.

Question 16

When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.

Question 17

The amount by which an objective function coefficient would have to improve before it would be possible for the corresponding variable to assume a positive value in the optimal solution is called the

A)reduced cost.
B)relevant cost.
C)sunk cost.
D)dual price.

Question 18

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.

Question 19

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.

Question 20

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

Question 21

The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.

Question 22

There is a dual price for every decision variable in a model.

Question 23

If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.

Question 24

Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.

Question 25

The dual price associated with a constraint is the improvement in the value of the solution per unit decrease in the right-hand side of the constraint.

Question 26

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

Question 27

Decision variables must be clearly defined before constraints can be written.

Question 28

The amount of a sunk cost will vary depending on the values of the decision variables.

Question 29

The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.

Question 30

A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective.

Question 31

For a minimization problem, a positive dual price indicates the value of the objective function will increase.