CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
1. The reduced cost (shadow price) for a positive decision
variable is 0. Answer: TRUE
2. When the right-hand sides of 2 constraints are both increased by 1 unit, the value
of the objective function will be adjusted by the sum of the constraints' prices.
Answer: FALSE
3. When a linear programming problem is solved using a computer package decision
variables will always be integer and therefore decision variable values never need to be
rounded.
Answer: FALSE
4. Sensitivity ranges can be computed only for the right hand sides of
constraints. Answer: FALSE
5. Sensitivity analysis determines how a change in a parameter affects the
optimal solution. Answer: TRUE
6. The sensitivity range for an objective function coefficient is the range of values over
which the current optimal solution point (product mix) will remain optimal.
Answer: TRUE
7. The sensitivity range for an objective function coefficient is the range of values
over which the profit does not change.
Answer: FALSE
8. The sensitivity range for a constraint quantity value is the range over which the shadow
price is valid. Answer: TRUE
9. If we change the constraint quantity to a value outside the sensitivity range for that
constraint quantity, the shadow price will change.
Answer: TRUE
10. The sensitivity range for a constraint quantity value is the range over which the
optimal values of the decision variables do not change.
Answer: FALSE
11. Linear programming problems are restricted to decisions in a single time
period. Answer: FALSE
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
12. A maximization problem may be characterized by all greater than or equal
to constraints. Answer: FALSE
13. A change in the value of an objective function coefficient will always change the
value of the optimal solution.
Answer: FALSE
14. The terms reduced cost, shadow price, and dual price all mean
the same thing. Answer: TRUE
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
15. Sensitivity analysis can be used to determine the effect on the solution for changing
several parameters at once.
Answer: FALSE
16. For a profit maximization problem, if the allowable increase for a coefficient in the
objective function is infinite, then profits are unbounded.
Answer: FALSE
17. The reduced cost (shadow price) for a positive decision variable is
. Answer:
zero
18. The sensitivity range for a is the range of values over
which the quantity values can change without changing the shadow price
Answer: constraint quantity Diff: 2
19. is the analysis of the effect of parameter changes on the
optimal solution. Answer: Sensitivity analysis
20. The sensitivity range for a constraint quantity value is also the range over which the
is valid.
Answer: shadow
price
21. The sensitivity range for an coefficient is the range of values over which the
current optimal solution point (product mix) will remain optimal.
Answer: objective function
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Consider the following linear program, which maximizes profit for two products, regular (R), and super
(S):
MAX 50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R
+ 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
1. The reduced cost (shadow price) for a positive decision
variable is 0. Answer: TRUE
2. When the right-hand sides of 2 constraints are both increased by 1 unit, the value
of the objective function will be adjusted by the sum of the constraints' prices.
Answer: FALSE
3. When a linear programming problem is solved using a computer package decision
variables will always be integer and therefore decision variable values never need to be
rounded.
Answer: FALSE
4. Sensitivity ranges can be computed only for the right hand sides of
constraints. Answer: FALSE
5. Sensitivity analysis determines how a change in a parameter affects the
optimal solution. Answer: TRUE
6. The sensitivity range for an objective function coefficient is the range of values over
which the current optimal solution point (product mix) will remain optimal.
Answer: TRUE
7. The sensitivity range for an objective function coefficient is the range of values
over which the profit does not change.
Answer: FALSE
8. The sensitivity range for a constraint quantity value is the range over which the shadow
price is valid. Answer: TRUE
9. If we change the constraint quantity to a value outside the sensitivity range for that
constraint quantity, the shadow price will change.
Answer: TRUE
10. The sensitivity range for a constraint quantity value is the range over which the
optimal values of the decision variables do not change.
Answer: FALSE
11. Linear programming problems are restricted to decisions in a single time
period. Answer: FALSE
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
12. A maximization problem may be characterized by all greater than or equal
to constraints. Answer: FALSE
13. A change in the value of an objective function coefficient will always change the
value of the optimal solution.
Answer: FALSE
14. The terms reduced cost, shadow price, and dual price all mean
the same thing. Answer: TRUE
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
15. Sensitivity analysis can be used to determine the effect on the solution for changing
several parameters at once.
Answer: FALSE
16. For a profit maximization problem, if the allowable increase for a coefficient in the
objective function is infinite, then profits are unbounded.
Answer: FALSE
17. The reduced cost (shadow price) for a positive decision variable is
. Answer:
zero
18. The sensitivity range for a is the range of values over
which the quantity values can change without changing the shadow price
Answer: constraint quantity Diff: 2
19. is the analysis of the effect of parameter changes on the
optimal solution. Answer: Sensitivity analysis
20. The sensitivity range for a constraint quantity value is also the range over which the
is valid.
Answer: shadow
price
21. The sensitivity range for an coefficient is the range of values over which the
current optimal solution point (product mix) will remain optimal.
Answer: objective function
, CHAPTER 3LINEAR PROGRAMMING: COMPUTER
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Consider the following linear program, which maximizes profit for two products, regular (R), and super
(S):
MAX 50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R
+ 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
