LINEAR PROGRAMMING:
SENSITIVITY ANALYSIS AND INTERPRETATION
OF SOLUTION
WITH ANSWERS RATED A+ DOWNLOAD TO
SCORE A
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
1
,2 Chapter 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.
, Chapter 8 LP Sensitivity Analysis and Interpretation of Solution 3
ANSWER: a
TOPIC: Dual price
9) A section of output from The Management Scientist is shown here.
Variabl Lower Limit Current Upper
e Value 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
10) A section of output from The Management Scientist is shown here.
Constra Lower Limit Current Value Upper Limit
t
in 2 240 300 420
SENSITIVITY ANALYSIS AND INTERPRETATION
OF SOLUTION
WITH ANSWERS RATED A+ DOWNLOAD TO
SCORE A
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
1
,2 Chapter 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.
, Chapter 8 LP Sensitivity Analysis and Interpretation of Solution 3
ANSWER: a
TOPIC: Dual price
9) A section of output from The Management Scientist is shown here.
Variabl Lower Limit Current Upper
e Value 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
10) A section of output from The Management Scientist is shown here.
Constra Lower Limit Current Value Upper Limit
t
in 2 240 300 420
